Methods for colorimetric analysis

ABSTRACT

A method includes determining the presence or concentration of an analyte in a sample. Determining the presence or concentration of an analyte in a sample includes receiving a first image containing an image of the sample, the first image obtained using an image sensor having two or more colour channels. Determining the presence or concentration of an analyte in a sample includes extracting first and second mono-colour arrays from the first image, the first and second mono-colour arrays corresponding to different colour channels of the image sensor, wherein each mono-colour array comprises one or more entries and each entry is determined by aggregating one or more pixels of the first image. Determining the presence or concentration of an analyte in a sample includes determining a filtered array based on the first and second mono-colour arrays, each entry of the filtered array calculated as a ratio of the corresponding entries of the first and second mono-colour arrays, or calculated as a difference of the corresponding entries of the first and second mono-colour images. Determining the presence or concentration of an analyte in a sample includes determining the presence or concentration of the analyte based on the filtered array.

RELATED APPLICATIONS

This application claims foreign priority benefits are under 35 U.S.C. §119(a)-(d) or 35 U.S.C. § 365(b) of British application numberGB1706572.3, filed Apr. 25, 2017, the entirety of which is incorporatedherein.

FIELD OF THE INVENTION

The present invention relates to methods of colorimetric analysis ofsamples which may comprise one or more analytes, each analyte having anassociated colour.

BACKGROUND

Biological testing for the presence and/or concentration of an analytemay be conducted for a variety of reasons including, amongst otherapplications, preliminary diagnosis, screening samples for presence ofcontrolled substances and management of long term health conditions.

Lateral flow devices (also known as “lateral flow immunoassays”) are onevariety of biological testing. Lateral flow devices may be used to testa liquid sample such as saliva, blood or urine, for the presence of ananalyte. Examples of lateral flow devices include home pregnancy tests,home ovulation tests, tests for other hormones, tests for specificpathogens and tests for specific drugs. For example, EP 0 291 194 A1describes a lateral flow device for performing a pregnancy test.

In a typical lateral flow testing strip, a liquid sample is introducedat one end of a porous strip which is then drawn along the strip bycapillary action (or “wicking”). A portion of the lateral flow strip ispre-treated with labelling particles that have been activated with areagent which binds to the analyte to form a complex (if the analyte ispresent in the sample). The bound complexes and any unreacted labellingparticles continue to propagate along the strip before reaching atesting region which is pre-treated with an immobilised binding reagentthat binds bound complexes of analyte and labelling particles and doesnot bind unreacted labelling particles. The labelling particles have adistinctive colour, or other detectable optical property such asfluorescence. The development of a concentration of labelling particlesin the test regions provides an observable indication that the analytehas been detected. Lateral flow test strips may be based on, forexample, colorimetric labelling using gold or latex nanoparticles.Fluorescent colorimetry employs marker molecules which fluoresce aspecific colour.

Another variety of biological testing involves assays conducted inliquids held in a container such as a vial, a PCR well or plate, acuvette or a microfluidic cell. Liquid assays may be measured based oncolorimetric measurements in reflection, transmission or fluorescencearrangements. An advantage of some liquid based assays is that they mayallow tests to be conducted using very small (e.g. picolitre) volumes.However, in such small volumes, the desired colour change orfluorescence may be difficult to detect.

Sometimes, merely determining the presence or absence of an analyte isdesired, i.e. a qualitative colorimetric test. In other applications, anaccurate concentration of the analyte may be desired, i.e. aquantitative colorimetric test. Mobile devices including cameras, forexample smart phones, have been widely adopted. It has been suggested toemploy such mobile devices to perform quantitative analysis of theresults of colorimetric lateral flow tests.

SUMMARY

According to a first aspect of the invention there is provided a methodincluding determining the presence or concentration of an analyte in asample. Determining the presence or concentration of an analyte in asample includes receiving a first image containing an image of thesample, the first image obtained using an image sensor having two ormore colour channels. Determining the presence or concentration of ananalyte in a sample includes extracting first and second mono-colourarrays from the first image, the first and second mono-colour arrayscorresponding to different colour channels of the image sensor, whereineach mono-colour array comprises one or more entries and each entry isdetermined by aggregating one or more pixels of the first image.Determining the presence or concentration of an analyte in a sampleincludes determining a filtered array based on the first and secondmono-colour arrays, each entry of the filtered array calculated as aratio of the corresponding entries of the first and second mono-colourarrays, or calculated as a difference of the corresponding entries ofthe first and second mono-colour images. Determining the presence orconcentration of an analyte in a sample includes determining thepresence or concentration of the analyte based on the filtered array.

Signals resulting from background inhomogeneity of the sample may bereduced or removed in the filtered array. In this way, both the minimumdetectable concentration of the analyte and the resolution with which aconcentration of the analyte may be determined may be improved.

Each pixel of each image obtained using the image sensor may include anintensity value corresponding to each colour channel.

Each entry of each mono-colour array may correspond to aggregating a rowor a column of the first image, to aggregating the pixels of the firstimage within a region of interest, or to a single pixel of the firstimage, wherein each mono-colour array may be a mono-colour image and thefiltered array may be a filtered image. Aggregating may includingsumming. Aggregating may including obtaining a mean, median or modeaverage.

Receiving the first image may include using the image sensor to obtainthe first image.

Determining the presence or concentration of an analyte in a sample mayinclude receiving a calibration array comprising one or more entries,each entry corresponding to a reference concentration of the analyte,wherein determining the presence or concentration of the analyte basedon the filtered array comprises comparing each entry of the filteredarray with one or more entries of the calibration array. The filteredarray and the calibration array need not have the same number ofentries.

Receiving the calibration array may include retrieving the calibrationarray from a storage device or storage location.

Receiving the calibration array may include using the image sensor toobtain a second image containing an image of a calibration sample, thecalibration sample including one or more calibration regions and eachcalibration region corresponding to a reference concentration of theanalyte. Receiving the calibration array may include extracting firstand second mono-colour calibration arrays from the second image, thefirst and second mono-colour calibration arrays corresponding todifferent colour channels of the image sensor, wherein each mono-colourcalibration array comprises one or more entries and each entry isdetermined by aggregating the pixels of the second image correspondingto a calibration region. Receiving the calibration array may includedetermining the calibration array based on the first and secondmono-colour calibration arrays, each entry of the calibration arraycalculated as a ratio of the corresponding entries of the first andsecond mono-colour calibration arrays, or as a difference of thecorresponding entries of the first and second mono-colour calibrationarrays. Aggregating may include summing. Aggregating may includeobtaining a mean, median or mode average.

According to a second aspect of the invention there is provided a methodincluding determining the presence or concentration of one or moreanalytes in a sample. Determining the presence or concentration of oneor more analytes in a sample includes receiving a first image containingan image of the sample, the first image obtained using an image sensorhaving two or more colour channels. Determining the presence orconcentration of one or more analytes in a sample includes extracting,from the first image, a mono-colour array corresponding to each colourchannel, wherein each mono-colour array comprises one or more entriesand each entry is determined by aggregating one or more pixels of thefirst image. Determining the presence or concentration of one or moreanalytes in a sample includes determining a mono-colour absorbance arraycorresponding to each colour channel, wherein each entry of eachmono-colour absorbance array is an absorbance value determined based onthe corresponding entry of the mono-colour array of the same colourchannel. Determining the presence or concentration of one or moreanalytes in a sample includes determining, for each entry of themono-colour absorbance arrays, a concentration vector by generating anabsorbance vector using the absorbance values from corresponding entriesof each of the mono-colour absorbance arrays, and determining theconcentration vector by multiplying the absorbance vector with ade-convolution matrix. Each concentration vector includes aconcentration value corresponding to each of the one or more analytes.

Each pixel of the first image may include an intensity valuecorresponding to each colour channel.

Each entry of each mono-colour array may correspond to aggregating a rowor a column of the first image, to aggregating the pixels of the firstimage within a region of interest, or to a single pixel of the firstimage, wherein each mono-colour array may be a mono-colour image and thefiltered array may be a filtered image. Aggregating may include summing.Aggregating may include obtaining a mean, median or mode average.

Receiving the first image may include using the image sensor to obtainthe first image.

The image sensor may include red, green and blue colour channels. Theimage sensor may include an infra-red colour channel. The image sensormay include cyan, yellow and magenta colour channels. The image sensormay include an ultraviolet colour channel.

The methods may be applied to each frame of a video, wherein receiving afirst image may include extracting a frame from the video.

The sample may be illuminated by ambient light. The sample may beilluminated using a light source.

The methods may include illuminating the sample using a light source,wherein the sample and image sensor are arranged to be screened fromambient light.

The light source may be a broadband light source. The light source mayinclude two or more types of light emitter, and each type of lightemitter may emit light of a different colour. The light source mayinclude an ultra-violet light source and the colour associated with theanalyte may arise from fluorescence.

The methods may include arranging the sample within a sample holderhaving a fixed geometric relationship with the image sensor. The methodsmay include arranging the sample within a sample holder having a fixedgeometric relationship with the image sensor and a light source.

The first image may be obtained using light transmitted through thesample. The first image may be obtained using light reflected from thesample. The second image may be obtained using light transmitted throughthe calibration sample. The second image may be obtained using lightreflected from the calibration sample.

The image sensor may form part of a camera. The light source may beintegrated into the camera.

The image sensor may form part of a mobile device.

The mobile device may include one or more processors, and the step ofdetermining the presence or concentration of an analyte or of one ormore analytes may be carried out by the one or more processors.

Receiving the first image may include receiving a full sensor imagewhich contains an image of the sample, identifying a first sub-region ofthe full sensor image which contains the sample and obtaining the firstimage by extracting the first sub-region.

Receiving the second image may include receiving a full sensor imagewhich contains an image of the calibration sample, identifying a secondsub-region of the full sensor image which contains the calibrationsample and obtaining the second image by extracting the secondsub-region.

The first and second sub-regions may correspond to different sub-regionsof the same full sensor image. The first and second sub-regions maycorrespond to sub-regions of different full sensor images. The firstand/or second sub-regions may be identified using computer visiontechniques. The sample may include registration indicia for use inidentifying the first and/or second sub-regions. The methods may alsoinclude arranging one or more objects on or around the sample and/or thecalibration sample, each object including registration indicia for usein identifying the first and/or second sub-regions.

According to a third aspect of the invention there is provided a methodof determining a de-convolution matrix, the method includes providing anumber, K, of calibration samples, wherein each calibration samplecomprises a known concentration of K different analytes. The methodincludes, for each calibration sample, determining, for each of a numberK of colour channels, the absorbance values of the calibration sample,generating an absorbance vector using the K measured absorbance valuesand generating a concentration vector using the K known concentrationsof analytes. The method also include generating a first K by K matrix bysetting the values of each column, or each row, to be equal to thevalues of the absorbance vector corresponding to a given calibrationsample. The method also includes inverting the first matrix. The methodalso includes generating a second K by K matrix by setting the values ofeach column, or each row, to be equal to the values of the concentrationvector corresponding to a given calibration sample. The method alsoincludes determining a deconvolution matrix by multiplying the secondmatrix by inverse of the first matrix. Each calibration sample may be aregion of a single, larger calibration sample.

BRIEF DESCRIPTION OF THE DRAWINGS

Certain embodiments of the present invention will now be described, byway of example, with reference to the accompanying drawings in which:

FIG. 1 illustrates a system for colorimetric analysis using reflectedlight;

FIG. 2 illustrates a system for colorimetric analysis using transmittedlight;

FIG. 3 shows a cross section of a lateral flow device for measurementsusing reflected light;

FIG. 4 shows a cross section of a lateral flow device for measurementsusing transmitted light;

FIGS. 5A to 5D illustrate filter mosaics for use in an image sensor;

FIG. 6 illustrated detection of a colour using an image sensor havingred, green and blue colour channels;

FIGS. 7 and 8 illustrate the structure of a porous strip for lateralflow devices shown in FIGS. 3 and 4;

FIG. 9 illustrates a background profile of reflectance from a blankporous strip;

FIGS. 10, 11 and 12 illustrate profiles of reflected intensity observedby green, blue and red colour channels respectively;

FIG. 13 illustrates combining intensity profiles from pairs of colourchannels to compensate for the background profile shown in FIG. 9;

FIG. 14 is a process flow diagram of a first method of obtaining afiltered image;

FIG. 15 illustrates a system for colorimetric analysis using a mobiledevice;

FIG. 16 shows experimental measurements of the background reflectancefrom a blank nitrocellulose strip;

FIG. 17 shows the reflectance of a nitrocellulose strip including anumber of test regions treated with gold nanoparticles for red, greenand blue colour channels;

FIG. 18 shows filtered data obtained by taking the difference of greenand red channel data shown in FIG. 17;

FIG. 19 is a photograph of the nitrocellulose strip corresponding to thedata shown in FIGS. 17 and 18;

FIG. 20 shows a comparison between filtered data calculated asdifferences and filtered data calculated as ratios;

FIG. 21 illustrates a second system for colorimetric analysis of acuvette;

FIG. 22 illustrates a third system for colorimetric analysis of an assayplate;

FIG. 23 illustrates a fourth system for colorimetric analysis of aflowing liquid;

FIG. 24 illustrates a fifth system for colorimetric analysis of amicrofluidic device;

FIG. 25 illustrates a typical organic photodetector sensitivity profileand green, red and near infrared light emission profiles typical oforganic light emitting diodes;

FIG. 26 illustrates typical absorbance profiles for gold nanoparticles,a blue dye and nitrocellulose fibres;

FIG. 27 illustrate assumed concentration profiles for goldnanoparticles, for a blue dye and for nitrocellulose fibres forming aporous strip;

FIG. 28 illustrates simulated organic photodetector signals obtainedbased on the data shown in FIGS. 51 to 53;

FIG. 29 illustrates filtering a simulate organic photodetector signalcorresponding to a green organic light emitting diode;

FIG. 30 illustrates filtering a simulate organic photodetector signalcorresponding to a near infrared organic light emitting diode;

FIGS. 31 and 32 illustrate converting normalised transmission values toabsorbance values;

FIGS. 33 and 34 illustrate estimating absorbance fingerprint valuescorresponding to gold nanoparticles and nitrocellulose fibres;

FIG. 35 illustrates analysing a three component simulated system usingfirst and second wavelengths; and

FIG. 36 illustrates analysing a three component simulated system usingfirst, second and third wavelengths.

DETAILED DESCRIPTION OF CERTAIN EMBODIMENTS

In the following description, like parts are referred to using likereference numerals.

Colorimetric analysis of a sample involves analysing the concentrationof a target analyte which may be present in the sample based on a colourassociated with the target analyte. The colour associated with thetarget analyte may be inherent to the target analyte. Alternatively, thecolour associated with the target analyte may be applied by, forexample, reacting the target analyte with a reagent having a colour orwith activated labelling particles. Colorimetric analysis may bequalitative, in other words concerned only with determining the presenceor absence of the target analyte. Colorimetric analysis may bequantitative, such that the concentration of the target analyte may bedetermined. In quantitative colorimetric analysis, a sample is typicallycompared against a calibration sample or standard sample whichcorresponds to a reference concentration of the target analyte.

In both qualitative and quantitative colorimetric analysis, the minimumthreshold for detecting a target analyte may be improved if the signalto noise ratio of the measurement could be improved. Additionally,improvements in the signal to noise ratio may also allow for theconcentration of a target analyte to be determined with improvedresolution during quantitative colorimetric analysis. In the presentspecification, noise is taken to refer to signals other than the desiredsignal, for example background inhomogeneity of a sample which maycontain the target analyte.

The present specification is concerned with improving thesignal-to-noise ratio for colorimetric analysis performed using an imagesensor such as a camera. In one example, colorimetric analysis using amobile device such as a smart phone or tablet computer may be conductedwith improved signal-to-noise ratio. A mobile device may provide a goodplatform for colorimetric analysis because mobile devices typicallyinclude a camera to obtain images and a light for illuminating a sample,in addition to memory and one or more processors for processing theimages according to the first or second methods of the presentspecification.

The present specification describes first and second methods by whichnon-specific background signals which are not associated with an analyteof interest may be filtered out in order to improve the signal-to-noiseratio of an image. The filtered image may then be used for colorimetricanalysis having an improved limit of detection (i.e. a lower minimumdetectable concentration) and also having improved resolution of theanalyte concentration. The present specification is based, at least inpart, on the realisation that many common sources of background signalmay be correlated between different colour channels, whereas the desiredsignal is usually not correlated or only weakly correlated betweendifferent colour channels.

Referring to FIG. 1, a system for colorimetric analysis 1 is shown.

An image sensor 2 is arranged to capture an image of a sample 3. Thesample 3 may contain a target analyte. The purpose of the system 1 is todetermine whether or not the sample 3 does contain the target analyteand/or in what concentration. The image sensor 2 is typically combinedwith optics (not shown) and integrated into a camera. The image sensor 2includes two or more colour channels.

A colour channel corresponds to a bandwidth of light to which anindividual sensor of the image sensor 2 is sensitive. In many digitalcameras different colour channels are provided by a filter mosaic (FIGS.5A to 5D) overlying an array of light sensors. Each image captured bythe image sensor 2 comprises an array of N by M pixels, where N and Mare both positive, non-zero integers. An image may be denoted by anarray I and the pixel corresponding to the n^(th) of N row and them^(th) of M column of I may be denoted as I_(n,m). Each pixel I_(n,m) ofeach image is made up of a set of intensity values which correspond toeach of the two or more colour channels. A pixel I_(n,m) may berepresented be a vector of corresponding intensity values, for example,I_(n,m)=(I_(n,m,1), . . . , I_(n,m,k), . . . , I_(n,m,K)) when the imagesensor includes K different colour channels, where k is an integerdenoting the k^(th) colour channel and 1≤k≤K. Intensity values I_(n,m,k)may take the form of measured voltages directly read from the imagesensor 2 or processed (and possibly re-balanced) intensity values, forexample, integer values between 0 and 255. Intensity values I_(n,m,k)may be normalised globally to the image I, i.e. divided by the peakintensity of any colour channel, of normalised internally, i.e. valuesI_(n,m,k) of the k^(th) of K colour channels are divided by the peakintensity of the k^(th) colour channel, i.e. max(I_(n,m,k)). Suchnormalisation of intensity values does not substantially affect themethods described hereinafter.

For example, a common type of digital camera includes an image sensor 2comprising three colour channels corresponding to red (R), green (G) andblue (B) light. This type of sensor shall be referred to herein as anRGB image sensor 2. In this case an image I is made up of pixelsI_(n,m)=(I_(n,m,R), I_(n,m,G), I_(n,m,B)).

An image I captured by the image sensor 2 may be easily separated into aset of mono-colour images or sub-images. For example, an image I from anRGB image sensor 2 may be divided into a red mono-colour image I^(R)which is an N by M array of the red intensity values I_(n,m,R), a greenmono-colour image I^(G) which is an N by M array of the green intensityvalues I_(n,m,G), and a blue mono-colour image I^(B) which is an N by Marray of the intensity values I_(n,m,B).

The purpose of the system 1 is to determine whether or not the targetanalyte is present in the sample 3, and/or to determine a concentrationof the target analyte. To this end, the sample 3 is arranged within thefield-of-view 4 of the image sensor 2 and the image sensor 2 is used toacquire a sample image I^(S) (or first image) which contains an image ofthe sample 3.

The sample image I^(S) may be obtained and processed immediately, forexample, using a single device which includes an image sensor 2 and dataprocessing capabilities. Alternatively, the sample image I^(S) may beobtained separately and in advance of applying the first or secondmethods described herein. For example, a number of sample images I^(S)may be obtained as a batch for subsequently batch processing at a latertime or in a different location. For example, one of more sample imagesI^(S) may be obtained then uploaded or transmitted to a remote locationfor processing.

First and second mono-colour arrays L¹, L² are extracted from the sampleimage I^(S) (or first image). The first and second mono-colour arraysL¹, L² correspond to different colour channels, for example the k₁ ^(th)and k₂ ^(th) of K colour channels where k₁≠k₂. Each mono-colour arrayL¹, L² includes a number, N_(e), of entries. Each entry of the first andsecond mono-colour arrays L¹, L² is determined by aggregating one ormore pixels I^(S) _(n,m) of the sample image I^(S). For example, eachentry of the mono-colour arrays L¹, L² may correspond to a row of thesample image I_(S), such that N_(e)=N and:

$\begin{matrix}{L_{n}^{k} = {\sum\limits_{m = 1}^{M}\; I_{n,m,k}^{S}}} & (1)\end{matrix}$in which L^(k) _(n) is the n^(th) of N entries of a mono-colour arraycorresponding to the k^(th) of K colour channels. Alternatively, eachentry of the mono-colour arrays L¹, L² may correspond to a column of thesample image I_(S) such that N_(e)=M.

Alternatively, each entry of the mono-colour arrays L¹, L² maycorrespond to a specific region of interest within the sample imageI^(S). Such a region of interest may be automatically determined or userdeterminable. A region of interest may be rectangular, for example,spanning rows na to nb and columns ma to mb such that:

$\begin{matrix}{L_{i}^{k} = {\sum\limits_{n = {na}}^{nb}\;\left( {\sum\limits_{m = {ma}}^{mb}\; I_{n,m,k}^{S}} \right)}} & (2)\end{matrix}$in which L^(k) _(i) is the i^(th) of N_(e) entries of a mono-colourarray corresponding to the k^(th) of K colour channels, and in which thei^(th) entry corresponds to a region of interest defined by na≤n≤nb andma≤m≤mb. In equations (1) and (2), aggregation is performed by summingpixel intensity values. However, aggregation may alternatively byperformed by obtaining a mean, median or mode average of correspondingpixel values I^(S) _(n,m,k) of the sample image I^(S).

Another option is that each entry of the mono-colour arrays L¹, L² maycorrespond to a single pixel of the sample image I^(S), in other wordsaggregating a single pixel so that L^(k) _(n,m)=I^(S) _(n,m,k). In thislatter case, the first and second mono-colour arrays L¹, L² areequivalent to first and second mono-colour images I¹, I². The firstmono-colour image I¹ is an N by M array of the intensity values I¹_(n,m)=I_(n,m,k) of one colour channel, for example the k₁ ^(th) of Kcolour channels. The second mono-colour image I² is an N by M array ofthe intensity values I² _(n,m)=I_(n,m,l) of a second, different colourchannel, for example the k₂ ^(th) of K colour channels.

In principle, any pair of colour channels of the image sensor 2 may beused to provide the first and second mono-colour arrays L¹, L² (ormono-colour images I¹, I²). In practice, one pairing of colour channelswill be preferred for each analyte, depending on the colour associatedwith the analyte and the colour balance of illumination. According tothe second method described hereinafter, more than two colour channelsmay be analysed.

For example, using an RGB image sensor 2 there are three possiblepairings of colour channels, namely R and G, R and B or G and B. For afirst analyte the optimal pairing might be R and G, whereas G and Bmight be the optimal pairing for a second analyte which is associatedwith a different colour than the first analyte.

Using the first and second mono-colour arrays L¹, L², a filtered arrayL^(F) may be calculated in several ways. In a first calculation, thei^(th) of N_(e) entries L^(F) _(i) of the filtered array L^(F) may becalculated as a ratio of the corresponding entries L¹ _(i), L² _(i) ofthe first and second mono-colour arrays L¹, L², for example accordingto:

$\begin{matrix}{L_{i}^{F} = \frac{L_{i}^{1}}{L_{i}^{2}}} & (3)\end{matrix}$and in the special case that the first and second mono-colour arrays L¹,L² are first and second mono-colour images I¹, I², the filtered arrayL^(F) is a filtered image I^(F) calculated according to:

$\begin{matrix}{I_{n,m}^{F} = \frac{I_{n,m}^{1}}{I_{n,m}^{2}}} & \left( {3b} \right)\end{matrix}$

Alternatively, in a second calculation, the i^(th) of N_(e) entriesL^(F) _(i) of the filtered array L^(F) may be calculated as a differenceof the corresponding entries L¹ _(i), L² _(i) of the first and secondmono-colour arrays L¹, L², for example according to:L _(i) ^(F) =L _(i) ¹ −L _(i) ²  (4)and in the special case that the first and second mono-colour arrays L¹,L² are first and second mono-colour images I¹, I², the filtered arrayL^(F) is a filtered image I^(F) calculated according to:I _(n,m) ^(F) =I _(n,m) ¹ −I _(n,m) ²  (4b)

In some examples the filtered array L^(F) calculated as a difference maybe calculated as a weighted difference of the corresponding entries L¹_(i), L² _(i) of the first and second mono-colour arrays L¹, L², forexample according to:

$\begin{matrix}{L_{i}^{F} = \frac{L_{i}^{1} - L_{i}^{2}}{L_{i}^{1} + L_{i}^{2}}} & (5)\end{matrix}$and in the special case that the first and second mono-colour arrays L¹,L² are first and second mono-colour images I¹, I², the filtered arrayL^(F) is a filtered image I^(F) calculated according to:

$\begin{matrix}{I_{n,m}^{F} = \frac{I_{n,m}^{1} - I_{n,m}^{2}}{I_{n,m}^{1} + I_{n,m}^{2}}} & \left( {5b} \right)\end{matrix}$

Image sensors 2 integrated into cameras typically output images inprocessed file formats. Commonly used file formats include jointphotographic experts group (“.jpeg”), bitmap (“.bmp”), tagged image fileformat (“.tiff”) and so forth. The methods of the present specificationmay be carried out on any such processed file formats which retaincolour information. Equally, the methods of the present specificationmay be carried out on raw image data files (no standardised filenameextension is in use) output by the image sensor 2. Raw image data filesmay provide superior signal-to-noise ratio when compared to processedfile formats, since compressed file formats can sometimes introduceadditional noise (compression artefacts) into the image data.

The presence or concentration of a target analyte in the sample 3 may bedetermined based on the filtered array L^(F) or filtered image I^(F). Asshall be explained hereinafter, in the filtered array L^(F) or imageI^(F), the influence of noise resulting from background inhomogeneity ofthe sample 3 may be substantially reduced. This may permit detection ofthe presence of a target analyte at a lower concentration, since smallersignals may be clearly distinguished above the reduced background noise.The precision of quantitative estimates of the target analyteconcentration may also be improved as a result of the reduced noise inthe filtered array L^(F) or image I^(F).

Lateral flow test devices (also known as “lateral flow test strips” or“lateral flow immunoassays”) are a variety of biological testing kit.Lateral flow test devices may be used to test a liquid sample, such assaliva, blood or urine, for the presence of a target analyte. Examplesof lateral flow devices include home pregnancy tests, home ovulationtests, tests for other hormones, tests for specific pathogens and testsfor specific drugs.

In a typical lateral flow test strip, a liquid sample is introduced atone end of a porous strip 5 and the liquid sample is then drawn alongthe porous strip 5 by capillary action (or “wicking”). One or moreportions of the porous strip 5 are pre-treated with labelling particles6 (FIG. 8) which are activated with a reagent which binds to the targetanalyte to form a complex if the target analyte is present in the liquidsample. The bound complexes and any unreacted labelling particles 6(FIG. 8) continue to propagate along the porous strip 5 before reachinga testing region 7 which is pre-treated with an immobilised bindingreagent that binds complexes of analyte bound to labelling particles 6(FIG. 8) and does not bind unreacted labelling particles 6 (FIG. 8). Thelabelling particles 6 (FIG. 8) have a distinctive colour, or otherwiseabsorb or fluoresce in response to one or more ranges of ultraviolet(UV), visible (VIS) or near infrared (NIR) light. The development of aconcentration of labelling particles 6 (FIG. 8) in the test region 7 maybe measured and quantified through colorimetric analysis, for example tomeasure the concentration of labelling particles 6 (FIG. 8). The porousstrip 5 may also include a control region 8 which is treated with animmobilised binding reagent that binds unreacted labelling particle 6.One or more testing regions 7 of a lateral flow test strip may be usedas regions of interest corresponding to entries of the first and secondmono-colour arrays L¹, L².

Colorimetric analysis may be performed on developed lateral flow tests,i.e. a liquid sample has been left for a pre-set period to be drawnalong the porous strip 5. Additionally or alternatively, colorimetricanalysis may be employed to perform kinetic (i.e. dynamic) time resolvedmeasurements of the optical density of labelling particles 6 (FIG. 8) inthe test region 7 of a lateral flow test.

A user must interpret the results of a lateral flow test by judgingwhether the test region 7 exhibits a change in colour, or by comparing acolour change of the test region 7 against one or more shades or coloursof a reference chart provided with the test. It can be difficult for aninexperienced user to read the test results. Consequently, there hasbeen interest in providing tools which can automatically read and/orquantify the results of lateral flow test devices (along with othertypes of colorimetric assays). The present specification is not directlyconcerned with any one method of performing a qualitative orquantitative colorimetric analysis. Instead, the methods of the presentspecification are concerned with improving the signal-to-noise ratio ofmethods of colorimetric analysis which involve obtaining and analysingimages of a sample 3. This is possible because calculating the filteredarray L^(F) or image I^(F) as described hereinbefore may reduce orremove the effects of background inhomogeneity of the sample 3.

The porous strip 5 is commonly made from nitrocellulose or paper(cellulose) fibres. Consequently, the porous strip 5 is non-homogenous,and this can give rise to variations in the backgroundreflectance/transmittance of the porous strip 5. Such backgroundinhomogeneity is superposed with the signal from the labelling particles6 (FIG. 8), and acts as a source of noise in colorimetric analysis oflateral flow devices. The pattern of background inhomogeneity istypically random and thus different for each porous strip 5.

The methods of the present specification may improve the accuracy andprecision of colorimetric analysis by filtering out backgroundinhomogeneity of a sample. As explained further in relation to FIG. 8,this is because background inhomogeneity of a sample is often largelyindependent of wavelength, whereas the absorbance of the labellingparticles 6 used for colorimetric testing typically shows considerablevariation with wavelength.

The methods of the present specification may be used when the sample 3is illuminated by ambient light, i.e. natural daylight or regular roomlighting. A separate, dedicated light source is not required. However,in some examples, ambient lighting may be augmented using a light source9 arranged to illuminate the sample 3.

In other examples, the sample 3 may be illuminated using a light source9 whilst the sample 3 and image sensor 2 are screened from ambientlight. For example, the sample 3, image sensor 2 and light source 9 maybe sealed in a room or a container to reduce or even entirely block outambient light. Screening of ambient light may be preferred forfluorescence measurements.

The light source 9 may be a broadband light source, i.e. a white lightsource such as a tungsten-halogen bulb. A broadband light source neednot be a thermal source, and alternative broadband light sources includea white light emitting diode (LED), a mercury fluorescent lamp, a highpressure sodium lamp and so forth.

Alternatively, the light source 9 may include several different types oflight emitter. For example, the light source 9 may be an array of LEDshaving different colour emission profiles.

Some analytes may fluoresce under ultraviolet light, or may be labelledusing reagents and/or particles which fluoresce under ultraviolet light.For such analytes, the light source 9 may be an ultraviolet lamp. Thefluorescence may not be visible under bright ambient illumination, inwhich case it may be preferable to screen the sample 3 and image sensor2 from ambient light.

In general, there is no need for the sample 3 and the image sensor 2 tobe held in a fixed or repeatable relative orientation. However, in someexamples it may be useful to arrange the sample 3 within a sample holder(not shown) which has a fixed geometric relationship with the imagesensor 2. For example, the sample holder (not shown) may take the formof a frame or scaffold to, or within, which the image sensor 2 andsample 3 may be secured. When a light source 9 is used, the sampleholder (not shown) may secure the sample 3 in a fixed geometricrelationship with the image sensor 2 and the light source 9.

As shown in FIG. 1, the image sensor 2 may be used to obtain sampleimages I^(S) using light reflected from the sample 3.

Referring also to FIG. 2, an alternative system for colorimetricanalysis 1 b is shown.

The methods of the present specification are not limited to reflectedlight, and may also be used when the image sensor 2 is used to obtainsample images I^(S) using light transmitted through the sample 3. Atransmitted light image may be obtained by holding the sample 3 upagainst an ambient light source such as the sun, a window or a lightbulb. More conveniently, a transmitted light image may be obtained byarranging the sample 3 between a light source 9 and the image sensor 2.

Referring also to FIG. 3, an example of a first lateral flow device 10suitable for measurements using reflected light is shown.

A brief summary of the operation of lateral flow devices may be helpful,in so far as it is relevant to understanding the background of theinvention. However details of the specific chemistries used to test forparticular analytes are not relevant to understanding the presentinvention and are omitted.

The first lateral flow device 10 includes a porous strip 5 divided intoa sample receiving portion 11, a conjugate portion 12, a test portion 13and a wick portion 14. The porous strip 5 is in contact with a substrate15, and both are received into a base 16. The substrate 9 may beattached to the base 16. In some examples the substrate 9 may beomitted. A lid 17 is attached to the base 16 to secure the porous strip5 and cover parts of the porous strip 5 which do not require exposure.The lid 17 includes a sample receiving window 18 which exposes part ofthe sample receiving portion 11 to define a sample receiving region 19.The lid 17 also includes a result viewing window 20 which exposes thepart of the test portion 13 which includes the test region 7 and controlregion 8. The lid and base 16, 17 are made from a polymer such as, forexample, polycarbonate, polystyrene, polypropylene or similar materials.

A liquid sample 21 is introduced to the sample receiving portion 19through the sample receiving window 18 using, for example, a dropper 22or similar implement. The liquid sample 21 is transported along from afirst end 23 towards a second end 24 by a capillary, or wicking, actionof the porosity of the porous strip 11, 12, 13, 14. The sample receivingportion 11 of the porous strip 5 is typically made from fibrouscellulose filter material.

The conjugate portion 12 has been pre-treated with at least oneparticulate labelled binding reagent for binding a target analyte toform a labelled-particle-analyte complex. A particulate labelled bindingreagent is typically, for example, a nanometre or micrometre sizedlabelling particle 6 (FIG. 8) which has been sensitised to specificallybind to the analyte. The labelling particles 6 (FIG. 8) provide adetectable response, which is usually a visible optical response such asa particular colour, but may take other forms. For example, particlesmay be used which are visible in infrared or which fluoresce underultraviolet light. Typically, the conjugate portion 12 will be treatedwith one type of particulate labelled binding reagent to test for thepresence of one type of analyte in the liquid sample 21. However,lateral flow devices 10 may be produced which test for two or moreanalytes using two or more varieties of particulate labelled bindingreagent concurrently. The conjugate portion 12 is typically made fromfibrous glass, cellulose or surface modified polyester materials.

As the liquid sample 21 flows into the test portion 13,labelled-particle-analyte complexes and unbound label particles arecarried along towards the second end 24. The test portion 13 includesone or more test regions 7 and control regions 8 which are exposed bythe result viewing window 20 of the lid 17. A test region 7 ispre-treated with an immobilised binding reagent which specifically bindsthe label particle-target complex and which does not bind the unreactedlabel particles. As the labelled-particle-analyte complexes are bound inthe test region 43, the concentration of the labelling particles 6 (FIG.8) in the test region 7 increases. The concentration increase causes thecolour or other indicator of the labelling particles 6 (FIG. 8) tobecome observable. If the test region 7 changes colour (or changescolour within a prescribed period), then the test for the presence ofthe analyte is positive. If the analyte is not present in the liquidsample 21, then the test region 7 does not change colour (or does notchange colour within a prescribed duration) and the test is negative.Alternatively, if the label particles emit a detectable signal, forexample by fluorescence, then the detected emission increases as theconcentration of labelling particles bound in the test region 7increases.

To provide distinction between a negative test and a test which hassimply not functioned correctly, a control region 8 is often providedbetween the test region 7 and the second end 24. The control region 8 ispre-treated with a second immobilised binding reagent which specificallybinds unreacted labelling particles 6 (FIG. 8) and which does not bindthe labelled-particle-analyte complexes. In this way, if the test hasfunctioned correctly and the liquid sample 21 has passed through theconjugate portion 12 and test portion 13, the control region 8 willchange colour.

The test portion 13 is typically made from fibrous nitrocellulose,polyvinylidene fluoride, polyethersulfone (PES) or charge modified nylonmaterials. Regardless of the specific material used, the fibrous natureof the test portion results in background inhomogeneities which registerin the measured reflectance and transmittance of the test portion 13.The method described hereinbefore in relation to equations (1) and (2)can help to improve signal-to-noise ratio by reducing or removing theeffects of such background inhomogeneities. Alternatively, more than twocolour channels may be used to generate a filtered image using thesecond method explained hereinafter.

The wick portion 14 provided proximate to the second end 24 soaks upliquid sample 21 which has passed through the test portion 13 and helpsto maintain through-flow of the liquid sample 21. The wick portion 14 istypically made from fibrous cellulose filter material.

Referring also to FIG. 4, an example of a second lateral flow device 25suitable for measurements using transmitted light is shown.

The second lateral flow device 25 is the same as the first lateral flowdevice 10, except that the second lateral flow device 25 furtherincludes a second result viewing window 26. The second result viewingwindow 26 is provided through the base 16 and is arranged opposite tothe result viewing window 20. In the second lateral flow device 25, thesubstrate 15 is transparent or translucent, and allows light to betransmitted through the test region 7 and control region 8 of the testportion 13 for imaging via the result viewing window 20.

Referring to FIG. 5A, a first filter mosaic 27 for an image sensor 2 isshown.

As discussed hereinbefore, an image sensor 2 having multiple differentcolour channels may be provided using a filter mosaic 27 overlying anarray of light sensors. Each such light sensor is sensitive to thewavelengths of light which are transmitted by the overlying filter. Thefirst filter mosaic is a Bayer filter (or RGBG filter) for ared-green-blue, or RGB image sensor 2. Only four repeating units of thefirst filter mosaic are shown in FIG. 5A. RGB image sensors 2 are themost commonly employed image sensors 2 used in digital cameras, smartphones and so forth. Alternative mosaics of R, G and B filters may beused.

Referring also to FIG. 5B, a second filter mosaic 28 for an image sensor2 is shown.

Although RGB image sensors 2 are commonly employed, other types of imagesensors 2 are possible which use alternative colour channels. Forexample, the alternative cyan (C), yellow (Y), magenta (M) colour schememay be used instead of an RGB colour scheme. The second filter mosaic 28is a CYYM filter mosaic for a CYM image sensor 2.

Referring also to FIG. 5C, a third filter mosaic 29 for an image sensor2 is shown.

Image sensors 2 are not restricted to only three colour channels, and agreater number of colour channels may be included. The third filtermosaic 29 includes R, G and B filters, and additionally includesinfrared (IR) filters. An infrared colour channel for an image sensorwill typically transmit near infrared (NIR) light. Including a colourchannel for IR/NIR can be useful for the methods of the presentspecification. In particular, materials which are different (visible)colours may often have very similar reflectance/transmittance at IR/NIRwavelengths. The third mosaic filter 29 is an RGBIR mosaic filter for anRGBIR image sensor 2.

Referring also to FIG. 5d , a fourth filter mosaic 30 for an imagesensor 2 is shown.

Image sensors 2 are not restricted to three visible colour channels.Some image sensors 2 may use filter mosaics which combine four differentvisible colour channels, for example, the fourth filter mosaic 30 is aCYGM filter mosaic for a CYGM image sensor 2.

An image sensor 2 may include non-visible colour channels other thanIR/NIR, for example an image sensor 2 may include an ultraviolet colourchannel.

In principle, any number of colour channels may be included on an imagesensor. In practice, there are limits on the minimum size of lightsensors making up the array of an image sensor 2. Consequently, if largenumbers of different colour channels were included, the minimum repeatsize of the filter mosaic would become large and the offset betweenimages corresponding to each colour channel may become unacceptable. Inpractice, only three visible colour channels are required to producecolour images.

Referring also to FIG. 6, detection of a colour by an RGBIR image sensor2 is illustrated.

The reflectance profile 31 associated with an analyte may peak at orclose to a typical wavelength of green light λ_(G). For example, thereflectance profile 31 may take the value R(λ_(G)) at a typicalwavelength of green light λ_(G). Similarly, the reflectance profile 31may take values R(λ_(B)), R(λ_(R)) and R(λ_(IR)) at typical wavelengthsof blue, red and infrared light λ_(B), λ_(R) and λ_(IR) respectively.

A filter mosaic such as the third filter mosaic 29 includes R, G, B andIR filters having respective filter transmittance profiles 32, 33, 34,35. Each filter transmittance profile 32, 33, 34, 35 transmits a rangeof wavelengths about the corresponding wavelength λ_(B), λ_(G), λ_(R),λ_(IR).

Since the reflectance profile 31 associated with an analyte may varyconsiderably with wavelength, the intensity recorded by the image sensor2 and which is associated with the analyte will vary between thedifferent mono-colour images I^(k) _(n,m). In contrast to this,background inhomogeneity of a sample 3 may vary much less withwavelength. For example, varying density the of fibrous materials usedfor the porous strip 5 of a lateral flow testing device may lead toirregular variations in the amount of reflected/transmitted light, butsuch variations do not have a strong dependence on wavelength.Consequently, comparing measured intensity values from a pair ofdifferent colour channels can allow the signal resulting from backgroundinhomogeneity to be reduced or removed.

Referring also to FIGS. 7 and 8, the structure of a porous strip 5 isschematically illustrated.

Referring in particular to FIG. 7, a test region 7 lies between firstand second positions x₁, x₂ in a direction x along the length of theporous strip 5.

Referring in particular to FIG. 8, the porous strip 5 is typicallyfibrous, for example, formed from a mat of fibres 36 such asnitrocellulose fibres. Within the test region 7, the immobilised bindingreagent binds complexes of analyte and labelling particles 6.

The fibres 36 may scatter and/or absorb light across a broad range ofwavelengths in an approximately similar way. This is the case for whitefibres 36 providing a substantially white porous strip 5. Stronglycoloured fibres 36 are, in general, not preferred for lateral flowdevices, since this would tend to amplify the existing challenges ofreading and/or quantifying the test results. For example, the proportionof green light 37 which is scattered by fibres 36 is approximately thesame as the proportion of red light 38 scattered by the fibres 36.However, the fibrous porous strip 5 is not uniform, and the density offibres 36 may vary from point to point along the porous strip 5. Suchbackground variations of scattering/absorbance due to the inhomogeneityof the porous strip 5 may limit the sensitivity of a measurement, i.e.the minimum detectable concentration of labelling particles 6.

By contrast, within the test region 7, the absorbance or scattering bythe labelling particle 6 may be substantially different between greenlight 37 and red light 38. For example, if the reflectance 31 of thelabelling particles 5 is similar to that shown in FIG. 6.

Referring also to FIGS. 9 to 13, a schematic example of applying thefirst method is illustrated.

The schematic examples shown in FIGS. 9 to 13 are based on the schematicreflectance profile 31 shown in FIG. 6.

Referring in particular to FIG. 9, the background profile 39 ofreflected intensity as a function of position x along a porous stripshows variability which arises from the inhomogeneity of the porousstrip 5. When rows of the sample image I^(S) are aligned parallel to theposition direction x, the background profile 39 corresponds to summingpixel intensity values in each column of the sample image I^(S) (andvice versa for rows and columns). The background profile 39 correspondsto no labelling particles 6 within the test region 7, x₁ to x₂. Forlarge concentrations of labelling particles 6, the peak-to-peakfluctuations of the background profile 39 will not prevent detection.However, at low concentrations of labelling particles 6, thepeak-to-peak fluctuations of the background profile 39 will preventreliable detection.

Referring in particular to FIG. 10, the reflected green intensity 40 isshown when a concentration of labelling particles 6 is bound within thetest region 7 substantially between positions x₁ to x₂. When rows of thesample image I^(S) are aligned parallel to the position direction x, thereflected green intensity 40 corresponds to a green mono-colour arrayL^(G), the entries of which are determined by summing pixel intensityvalues in each column of the sample image I^(S) (and vice versa for rowsand columns). The reflected green intensity 40 includes a contributionfrom the background profile 39 in addition to the reflections 41 arisingfrom the concentration of the labelling particles 6 within the testregion 7 substantially between positions x₁ to x₂.

Referring in particular to FIG. 11, the reflected blue intensity 42includes a contribution from the background profile 39 in addition tothe reflections 43 arising from the concentration of the labellingparticles 6 within the test region 7, x₁ to x₂. When rows of the sampleimage I^(S) are aligned parallel to the position direction x, thereflected blue intensity 42 corresponds to a blue mono-colour arrayL^(B), the entries of which are determined by summing pixel intensityvalues in each column of the sample image I^(S) (and vice versa for rowsand columns).

Referring in particular to FIG. 12, the reflected red intensity 44includes a contribution from the background profile 39 in addition tothe reflections 45 arising from the concentration of the labellingparticles 6 within the test region 7, x₁ to x₂. When rows of the sampleimage I^(S) are aligned parallel to the position direction x, thereflected red intensity 44 corresponds to a red mono-colour array L^(R),the entries of which are determined by summing pixel intensity values ineach column of the sample image I^(S) (and vice versa for rows andcolumns).

Referring now to FIG. 13, the method of equation (4) may be applied tothe difference of the green intensity 40 and the red intensity 44 toproduce an G-R filtered profile 46. When rows of the sample image I^(S)are aligned parallel to the position direction x, the G-R filteredprofile 46 corresponds to a filtered array L^(F). In this way, theinfluence of the background profile 39 may be reduced or removed. Inpractice, the R-G filtered profile 46 (i.e. the filtered array L^(F))will retain noise from other sources which, unlike the backgroundprofile 39, is not correlated between the green intensity 40 and the redintensity 44. Additionally, the background profile 39 may have somewavelength dependence in practice. The method of equation (4) may alsobe applied to the difference of the green intensity 40 and the blueintensity 42. However, since the difference in the reflectance profile31, i.e. R(λ_(G))−R(λ_(B)), for G-B is less than for G-R, the resultingG-B filtered profile 47, which is another example of a filtered arrayL^(F), has a smaller amplitude than the G-R filtered profile 46, so thatthe improvement in signal to noise ratio is less pronounced.

In general, any pair of channels may be selected as the first and secondmono-colour arrays L¹, L² or images I¹, I² to permit reduction orremoval of the background profile 39. However, in order to maximise theresultant signal due to an analyte, the pair of colour channels selectedto provide the first and second mono-colour arrays L¹, L² or images I¹,I² should preferably be chosen according to the largest differencebetween the transmittance profile 31 of the analyte and/or associatedlabelling particles 6.

Although the example described with reference to FIGS. 6 to 13 refers toimages obtained in a reflection geometry, the same principles apply to atransmission geometry, with substitution of the reflectance profile 31of the analyte for the transmittance profile (not shown). Both thetransmittance and reflectance depend upon the absorbance of the analyteor the associated labelling particles 6.

In this way, the signal-to-noise ratio of a signal associated with ananalyte may be improved in a filtered array L^(F) or image I^(F),whether the sample image I^(S) (first image) is obtained in transmissionor reflection.

Referring to FIG. 14, a process flow diagram of the first method ofdetermining the presence or concentration of an analyte in a sample 3 isshown.

Referring again to FIGS. 1 and 2, the method is conducted using an imagesensor 2 having two or more colour channels. Each pixel I_(n,m) of eachimage comprises a set of intensity values I_(n,m)=(I_(n,m,1), . . . ,I_(n,m,k), . . . , I_(n,m,K)) corresponding to each of the differentcolour channels.

The image sensor 2 is used to obtain a sample image I^(S), or firstimage, of the sample 3 which may comprise a target analyte (step S1).The target analyte has an associated colour. The associated colour maybe inherent to the target analyte. Alternatively, the associated colourmay be provided by a reagent which is reacted with the target analyte inadvance of obtaining the sample image I^(S). The associated colour maybe provided by labelling particles 6 which have been bound to the targetanalyte. If desired, the sample 3 may be secured in a sample holderhaving a fixed geometric relationship with the image sensor 2 beforeobtaining the sample image I^(S).

The first and second mono-colour arrays L¹, L² or images I¹, I² areextracted from the sample image I^(S) (step S2). For example,mono-colour arrays L¹, L² may be calculated in accordance with equations(1) or (2). In another example using an RGB image sensor 2 having pixelsI_(n,m)=(I_(n,m,R), I_(n,m,G), I_(n,m,B)), if the green and red colourchannels are to be used, a first mono-colour image I¹ may have pixelvalues I¹ _(n,m)=I_(n,m,R), and a second mono-colour image I² may havepixel values I² _(n,m)=I_(n,m,G).

The filtered array L^(F) or image I^(F) or second image is calculatedbased on the first and second mono-colour arrays L¹, L² or images I¹, I²respectively (step S3). Each entry of the filtered array L^(F), may becalculated as a ratio of the corresponding entries L¹ _(i), L² _(i) ofthe first and second mono-colour arrays L¹, L² according to equation(3). When mono-colour images I¹, I² are used, each pixel of the filteredimage I^(F) _(n,m) may be calculated as a ratio of the correspondingpixel values I¹ _(n,m), I² _(n,m) of the first and second mono-colourimages I¹, I² according to equation (3b). Alternatively, each entry ofthe filtered array L^(F) _(i) may be calculated as a difference of thecorresponding entries L¹ _(i), L² _(i) of the first and secondmono-colour arrays L¹, L² according to equation (4). When mono-colourimages I¹, I² are used, each pixel of the filtered image I^(F) _(n,m)may be calculated as a difference of the corresponding pixel values I¹_(n,m), I² _(n,m) of the first and second mono-colour images I¹, I²according to equation (4b). The difference may be a weighted differenceaccording to equations (5) or (5b) respectively.

If further samples 3 (or different regions of the same sample 3) requireanalysis (step S4, Yes), then such further samples 3 may be arranged topermit obtaining further sample images I^(S) using the image sensor(step S1).

The steps S1 to S4 provide a qualitative colorimetric analysis in whichthe limit of detection, i.e. the minimum detectable concentration ofanalyte, of the filtered array L^(F) or image I^(F) may be improved bythe reduction or removal of signals resulting from backgroundinhomogeneity of the sample 3.

If a quantitative analysis is required, comparison is usually made witha reference or standard calibration sample which corresponds to a knownconcentration of the analyte. This requires additional steps compared toa qualitative analysis.

Referring also to FIG. 15, the concentration of an analyte present inthe sample 3 may be determined by comparing the filtered array L^(F) orimage I^(F) with a calibration array J corresponding to a calibrationsample 54 (step S3 a). The calibration sample 54 may, in general,include one or more calibration regions 56. Each calibration region 56corresponds to a different reference concentration of the analyte. Thecalibration array J includes a number N_(c) of entries J_(d), being thed^(th) of N_(c) entries. Each entry J_(d) of the calibration array Jcorresponds to the reference concentration of a correspondingcalibration region 56. The calibration sample 54 may be the same as thesample 3, for example, both the sample 3 and calibration sample 54 couldbe porous strips 5. The difference being that a concentration of thecalibration sample 54 is known. Alternatively, the calibration sample 54may comprise a substrate having a region or area which has been printedor coloured so as to correspond to the same colour and shade as areference concentration of the analyte.

The calibration array J should have been generated according to asimilar method and in comparable conditions to the filtered array L^(F)or image I^(F) in order to permit direct comparisons. Otherwise, therelative intensities in the filtered array L^(F) or image I^(F) cannotbe meaningfully compared to those of the calibration array J. Theconcentration of analyte corresponding to an entry L^(F) _(i) or pixelI^(F) _(n,m) is determined by comparing the entry L^(F) _(i) or pixelI^(F) _(n,m) value against one or more entries J_(d) of the calibrationarray. In general, the calibration array J only needs a single entry andthe number of entries N_(c) in the calibration array J need not equalthe number of entries of in the filtered array L^(F).

For example, the concentration corresponding to an entry L^(F) _(i) maybe obtained based on a ratio of the entry L^(F) _(i) and a single entryJ_(d) of the calibration array J. When N_(c)>1, such a ratio may beobtained based on the entry J_(d) which is closest in value to the entryL^(F) _(i). Alternatively, the concentration corresponding to an entryL^(F) _(i) may be interpolated based on a pair of entries J_(d1), J_(d2)which bracket the entry L^(F) _(i).

A method of generating the calibration array J is explained withreference to steps Soa to Sod shown in FIG. 14.

The image sensor 2 is used to obtain a calibration image I^(C), orsecond image, containing an image of the calibration sample 54 (stepSoa).

Optionally, the optimal pair of colour channels for use in theprevailing illumination conditions (step Sob). For example, with an RGBimage sensor 2, filtered images corresponding to at least eachcalibration region 56 may be determined using the first method and allpossible pairs of colour channels, i.e. RG, RB or GB. Such filteredimages I^(F) may be analysed to determine relative improvements insignal-to-noise ratio for each, and the pair provided the largestimprovement may be selected as the optimal choice for use in theprevailing illumination conditions. The selected pair of colour channelsmay be used for determining both the calibration array J and thefiltered array L^(F) or filtered image I^(F) of the sample 3.

In this way, differences in the colour balance of ambient illuminationbetween different time and at different locations may be taken intoaccount and the pair of colour channels used for filtering may beselected to provide the optimal signal-to-noise ratio of a signalcorresponding to the analyte. In other examples, the pair of colourchannels to be used may be predetermined.

First and second mono-colour calibration arrays Lc¹, Lc² are extractedfrom the calibration image I^(C) (step Soc). This process is the sameway as extracting the mono-colour arrays L¹, L² from the sample imageI^(S), except that each entry of the mono-colour calibration arrays Lc¹,Lc² is determined by aggregating the pixels of the calibration imageI^(C) corresponding to one of the calibration regions 56.

The entries J_(d) of the calibration array J are calculated based on thefirst and second mono-colour calibration arrays Lc¹, Lc² by analogy towhichever of equations (3), (4) or (5) will be/has been used todetermine the filtered array L^(F) or image I^(F) (step Sod).

In examples where the sample 3 is secured in a sample holder (not shown)having a fixed geometric relationship with the image sensor 2, acalibration image I^(C) may be obtained using a calibration sample 54and the calibration array J calculated immediately prior to obtainingsample images I^(S) of one or more samples 3 which may contain theanalyte. The sample holder (not shown) may permit the calibration sample54 to be imaged in the same relative location as samples 3 to be tested.In-situ calibration allows for variations in ambient illumination to beaccounted for. When ambient illumination is used alone or in combinationwith a light source 9, it is preferable that the calibration image I^(C)be obtained at the same or a proximate location and immediately prior toobtaining sample images I^(S) of a set of samples 3, in order to ensurethat illumination conditions are comparable. Alternatively, thecalibration image I^(C) may be obtained at the same or a proximatelocation and immediately after obtaining sample images I^(S) of a set ofsamples 3. In this latter case, the processing of sample images I^(S)containing the sample 3 or samples 3 may be deferred to allow batchprocessing based on comparisons against the calibration image I^(C).

When ambient illumination is screened from the image sensor 2 and thesample 3 or calibration sample 54 and illumination is provided only alight source 9, the reproducible illumination conditions may permit thecalibration array J to be determined in advance and stored in a storagedevice or storage location (not shown). When required for quantificationof filtered arrays L^(F) or images I^(F), the calibration array J may beretrieved from the storage device or storage location.

Using a pair of colour channels provides a simple method to improve thesignal-to-noise ratio for samples 3 which may contain a singleanalyte/marker. When a sample 3 or a liquid sample is coloured (e.g.blood or urine), or when more than one analyte may be present in thesample 3, a second method utilising more than two colour channels anddescribed hereinafter may exhibit further performance improvements overthe first method.

Application of the Method to Colorimetric Analysis Using a Mobile Device

Referring in particular to FIG. 15, a system 48 for colorimetricanalysis using a mobile device is shown.

A mobile device 49, for example a smartphone, includes a camera havingan image sensor 2 (FIG. 1). The image sensor 2 (FIG. 1) may be an RGBimage sensor, a CYM image sensor 2, an RGBIR image sensor 2 and soforth.

An example of a sample 3 in the form of a first lateral flow device 10may be imaged using the camera of the mobile device 49 to obtain thesample image I^(S) (step S1 in FIG. 14). Such an image 50 may also beshown on the display 51 of the mobile device 49.

A flash LED integrated into the mobile device 29 may provide a lightsource 9 for illuminating the lateral flow device 10 in addition to, orinstead of, ambient light.

The mobile device 49 includes one or more processors (not shown). Thestep of extracting the first and second mono-colour arrays L¹, L² orimages I¹, I² (step S2 in FIG. 14) may be carried out by the one or moreprocessors (not shown). The step of determining the filtered array L^(F)or image I^(F) based on the first and second mono-colour arrays L¹, L²or images I¹, I² respectively (step S3 in FIG. 14) may be carried out bythe one or more processors (not shown) of the mobile device 49.

If the computing power of the mobile device 49 is sufficient, a previewimage displayed on the display 51 may show filtered images I^(F) insteadof the initial, unprocessed sample image I^(S) before the camera of themobile device 49 is activated to obtain an image. This may help a userto arrange the mobile device 49 in the right position with respect tothe lateral flow device 10.

In this way, the mobile device 49 may be used to perform qualitativecolorimetric analysis of the lateral flow device 10 with an improvedlimit of detection provided by use of the filtered array L^(F) or imageI^(F).

Where quantitative colorimetric analysis is desired, the step ofdetermining a concentration of the analyte (step S3 a in FIG. 14) may becarried out by the one or more processors. The mobile device 49 may beused to obtain a calibration image I^(C) and calibration array J (stepsSoa to Sod in FIG. 14). The calibration image I^(C) may be obtained andthe calibration array J determined either before or after obtaining oneor more sample images I^(S).

The sample image I^(S) processed to determine the filtered array L^(F)or image I^(F) need not be the entire frame of the image sensor 2 (FIG.1). For example, the mobile device 49 (FIG. 1) may be used to obtain afull sensor image I^(FS) which corresponds to the whole field of view 4of the camera (not shown) and which contains an image of the sample 3,10. A first sub-region 52 of the full sensor image I^(FS) may beidentified which contains the sample 3, and the sample image I^(S)(first image) may be obtained by extracting the first sub-region 52. Thefirst sub-region 52 may be identified by the one or more processors (notshown) of the mobile device 49 using computer vision techniques.

In order to improve the accuracy of identifying the first sub-region 52,the sample 3 may include registration indicia or marks 53 for use inidentifying the first sub-region 52. For example, registration indicia53 may be arranged to outline or bracket the result viewing window 20 ofthe lateral flow device 10.

If the sample 3 does not include registration indicia 53, one or moreobjects (not shown) which include registration indicia 53 may bearranged on or around the sample 3 to demark the first sub-region 52.

An advantage of using sub-regions of a full sensor image I^(FS) is thatthe need to obtain separate calibration images I^(C) may be avoided.

For example, a calibration sample 54 may be arranged next to the lateralflow device 10. The calibration sample 54 may take a similar form to thelateral flow device 10, with a casing provided with a viewing window 55through which a porous strip 5 supported in the casing may be viewed.The calibration sample 54 differs from the lateral flow device 10 inthat the porous strip 5 of the calibration sample 54 includes a numberof calibration regions 56, for example first, second and thirdcalibration regions 56 a, 56 b, 56 c. Each calibration region 56 a, 56b, 56 c is treated with a different reference concentration of labellingparticle 6. The concentration of the test region 7 may be determined orinterpolated from the known concentrations of the calibration regions 56a, 56 b, 56 c by comparing the relative entries of the filtered arrayL^(F) or pixel of the filtered image I^(F) against the entries of thecalibration array J determined based on the calibration image I^(C).

Only one calibration region 56 is needed for quantitative analysis.However, two or more calibration regions 56 spanning a range ofconcentrations may help to provide for more accurate quantification ofthe concentration of an analyte in the test region 7.

When the calibration sample 54 is arranged next to the sample 3 in theform of a lateral flow device 10, the sample image I^(S) may beextracted from the full sensor image I^(FS) as described hereinbefore.In the same way, the calibration image I^(C) (second image) may besimilarly extracted from the same full sensor image I^(FS) byidentifying a second sub-region 57 which contains the calibrationregions 56 a, 56 b, 56 c. The calibration sample 54 may also includeregistration indicia 53 for identifying the second sub-region 57.Registration indicia 53 identifying the first and second sub-regions 52,57 are preferably distinguishable through the application of computervision techniques if intended to be used in the same image. For example,the registration indicia 53 may demark different areas or shapes toindicate the first and second sub-regions 52, 57.

The preceding example has been explained with reference to a mobiledevice 49 and a lateral flow device 10 with images obtained inreflection. The same methods are equally applicable to images obtainedin transmission. A mobile device 49 need not be used, and any digitalcamera may be used to obtain the sample images I^(S), calibration imagesI^(C) and/or full sensor images I^(FS). Images may be processed and/orquantified by the same digital camera if it includes sufficientprocessing capacity.

Alternatively, where a mobile device 49 or other digital camera is used,all necessary images may be obtained without any processing by thedevice incorporating the image sensor 2. The images may subsequently beloaded onto a suitable data processing apparatus for processing todetermine filtered images I^(F) and calibration images I^(C).

Experimental Results

Experimental work to verify the method of improving signal-to-noiseratio has been carried out using mobile device 49 in the form of a smartphone having an RGB camera and which is capable of exporting image datain .jpeg and raw data formats.

Experiments were carried out using samples in the form of porous strips5 made from nitrocellulose. Such porous strips 5 are commonly employedin lateral flow devices 10, 25. Images were captured so that the rows ofpixels each image were substantially aligned with a long side of arectangular porous strip. Experiments were conducted using blank porousstrips 5 and also on porous strips 5 including test regions 58 (FIG. 19)which had been treated with varying concentrations ofgold-nanoparticles. Gold nanoparticles are commonly employed aslabelling particle 6 in lateral flow devices 10.

The experimental samples only varied in one direction, x, parallel tothe long side of the rectangular nitrocellulose strips. For ease ofvisualisation and presentation, data shall be presented by summing eachimage column into a single value. Given the one dimensional variabilityof the experimental samples, this does not remove important information.The same approach could also be applied to lateral flow devices 10, 25in general if the image rows align with the flow direction.

Referring to FIG. 16, the intensity (normalised) of a blank porous strip5 was obtained as a function of distance x parallel to the long side ofthe porous strip using red and green colour channels.

The red channel intensity profile 58 (solid line in FIG. 16) and thegreen channel intensity profile 59 (dashed line in FIG. 16) show similarfeatures corresponding to background inhomogeneity of the blank porousstrip 5. In terms of the previous notation, the red channel profile 59corresponds to a mono-colour array L^(R) with entries:

$\begin{matrix}{L_{n}^{R} = {\sum\limits_{m = 1}^{M}\; I_{n,m,R}^{S}}} & (6)\end{matrix}$and similarly for the green channel profile. With the green channel asthe first mono-colour array L^(G)=L¹ and the red channel as the secondmono-colour array L^(R)=L², a filtered profile 60 (dotted line in FIG.16) was calculated according to equation 3. It may be observed thatbackground inhomogeneity of the blank porous strip 5 has beensubstantially removed from the filtered profile 60.

Referring to FIGS. 17, 18 and 19, the application of the methods ofreducing signal-to-noise ratio is illustrated in FIGS. 17 and 18 inrelation to a porous strip 5 including a number of test regions 58 a, 58b, 58 c, 58 d, 58 e and shown in FIG. 19.

Referring in particular to FIG. 17, intensity profiles 62, 63, 64corresponding to red, green and blue colour channels respectively(solid, dashed and dotted lines in FIG. 17) were obtained in the mannerdescribed in relation to FIG. 16. The test regions 58 corresponding togreater concentrations of gold nanoparticles may be readily observed.However, as the concentration of gold nanoparticles is reduced, itbecomes difficult to clearly differentiate the test regions 58 amongstthe background inhomogeneity of the porous strip 5.

Referring in particular to FIG. 18, a filtered profile 65 obtained as adifference between the red intensity profile 62 and the green intensityprofile 63 is shown. It may be observed that the backgroundinhomogeneity of the porous strip 5 has been substantially reduced. Inthe filtered profile 65, even the test regions 58 corresponding to thelowest concentrations of gold nanoparticles are clearly distinguishable.

Referring to FIG. 20, filtered profiles calculated as differences andratios are compared.

The total intensity profile 66 (dotted line in FIG. 20) for a blankporous strip 5 (magnitude of a vector of the Red, Green and Blueintensities) exhibits the background inhomogeneity typical of porousstrips 5. In order to examine the differences between obtaining a ratioas opposed to a difference, a ratio filtered profile 67 (solid line inFIG. 20) was calculated according to equation (3) and a weighteddifference filtered profile 68 (dashed line in FIG. 20) was calculatedaccording to equation (4). In both cases, the first and secondmono-colour arrays L¹, L² were obtained using green and red colourchannels respectively, i.e. L¹=L^(G) and L²=L^(R). It may be observedthat either filtered profile 67, 68 substantially reduces the magnitudeof background variations (noise). Moreover, the ratio filtered profile67 and the weighted difference filtered profile 68 differ by less thanthe magnitude of residual background variations (residual noise).

Alternative Samples Types

Although examples have been described in relation to lateral flowdevices 10, 25, the methods disclosed herein can also be used with othertypes of sample 3 which minimal modifications.

For example, referring also to FIG. 21, a second system 69 forcolorimetric analysis is shown.

The second system 69 includes a sample 3 in the form of a container, forexample a cuvette 70, containing a liquid sample 71. The liquid sample71 may be illuminated by a light source 9 and the colour of the liquidsample 71 may be measured using the image sensor 2 in a transmissionarrangement. The signal-to-noise ratio may be improved for the secondsystem 69 using the methods of the present specification. Similarly, thesecond system 69 may be used for fluorescence assays as describedhereinbefore.

The difference in the second system 69 is that instead of scattering byfibres 36, the correction removes the effects of dust, scratches,smudges and so forth on the sides of the cuvette 70. Additionally, thesecond system 69 can correct for varying quantities of suspendedparticulate matter 72 (FIG. 23) in the liquid sample 71. For example,samples from a body of water may be obtained to check the concentrationsof a dissolved pollutant. Liquid samples 71 taken at different times mayinclude differing amounts of silt or other particles in suspension.Although samples may be left to allow suspended particulate matter 72(FIG. 23) to sediment out, this is impractical for field-testing. Usingthe methods of the present specification, the scattering from suspendedparticulate matter 72 (FIG. 23) may be reduced or removed by filtering.In this way, the hereinbefore described methods may be used to speed upthe process of analysing liquid samples 71 which show inherentvariability due to, for example, suspended particulate matter 72 (FIG.23).

Referring also to FIG. 22, a third system 73 for colorimetric analysisis shown.

The third system 73 includes a sample 3 in the form of an assay plate74. The assay plate 74 includes a transparent base 75. A number ofhollow cylinders 76 extend perpendicularly from the transparent base 75to provide a number of sample wells 77, for example a first sample well77 a, second sample well 77 b and so forth. Each sample well 77 may beprovided with a different liquid sample 71. For example, the firstsample well 77 a may hold a first liquid sample 71, the second samplewell 77 b may hold a second liquid sample 71 and so forth. The samplewells 77 may extend in one direction. More typically, the sample wells77 extend in two directions to form an array. The light source 9 may beused to illuminate the transparent base of the sample wells 7, and theimage sensor 2 may be used to capture an image of all or some of thesample wells 7.

The colour of each well may be analysed. Using the methods of thepresent specification, the signal-to-noise ratio may be improved. Thiscan allow colorimetric analysis of all or part of an assay plate 74 tobe analysed concurrently.

When the sample 3 is in the form of an assay plate 70, the sources ofinhomogeneity giving rise to a background profile 39 are not fibres 36.Similarly to the cuvette 70, dust, scratches, smudges and so forth onthe assay plate 74 surfaces may cause unwanted scattering.

Referring also to FIG. 23, a fourth system 78 for colorimetric analysisis shown.

The fourth system 78 includes a sample 3 in the form of a channel 79through which a liquid sample 71 flows. The channel 79 is defined bywalls 80 and includes windows 81 to permit the light from a light source9 to cross the channel 79 and be imaged by an image sensor 2.Alternatively, if the walls 80 are transparent, windows 81 may not beneeded. The channel 79 may be a pipe. Liquid flows through the channel79 in a flow direction 82. The liquid may include suspended particulatematter 72, for example silt in river water.

The fourth system 78 may be used to analyse the concentration of apollutant, or other analyte, which is present in the liquid flowingthrough the channel. The pollutant or other analyte may absorb atnon-visible wavelengths, and may be imaged using an infrared orultraviolet light source 9 and detected using an image sensor 2 havingsuitable colour channels. In general, the quantity of particulate matter72 suspended in liquid flowing through the channel 79 may vary withtime. Inhomogeneity in the background absorbance/scattering due tosuspended particulate matter 72 can have a detrimental effect on boththe limit of detection and the resolution of detecting the monitoredpollutant or other analyte. The signal due to the particulate matter 72may be reduced or removed by applying the filtering methods describedhereinbefore.

Referring also to FIG. 24, a fifth system for colorimetric analysis isshown.

The fifth system 83 is a microfluidic system used for sorting droplets84 which may contain a target analyte. Droplets 84 a, 84 b flow along achannel 85 through in a flow direction 86. Some droplets 84 a includethe target analyte whilst other droplets 84 b do not. At a T junction87, the droplets 84 a, 84 b are sorted according to the presence orabsence of the analyte by applying suction to either a first exit port88 or a second exit port 89. The sorting of the droplets 84 a, 84 b maybe based on colorimetric analysis of the droplets 84 a, 84 b approachingthe T-junction 87. Where the channels defining the fifth system are madeof transparent material, the colorimetric analysis may be performed byilluminating the fifth system 8 ₃ from below and obtaining an image fromabove. The fifth system 8 ₃ may operate based on fluorescence of thedroplets 84 a containing the analyte, in which case an ultraviolet lightsource 9 may be used.

The hereinbefore described methods can also be used to filter outbackground inhomogeneity of the fifth system. For example, the wallsdefining the channel 85 may be scratched or irregular, and dust orsurface scratches may also result in unwanted background variations.Using the hereinbefore described methods the signal-to-noise ratio forimages of the fifth system may be improved. This may allow moresensitive and/or more accurate sorting of the droplets 84 a, 84 b.

Second Method

For some tests, it may be desirable to detect and quantify theconcentrations of two or even more than two analytes in the same sample3 concurrently. A description follows of a second method, which is amethod of determining the presence or concentration of one or moreanalytes in a sample.

Additionally or alternatively, many samples which may contain one ormore analytes of interest may be coloured, for example blood. Othersamples 3 may display a range of colours depending on a concentrationof, for example, urine or other biologically derived substances orbyproducts. Additionally, the material of a porous strip 5 may have aslight coloration such that the reflectance/transmittance of the porousstrip 5 at different wavelengths varies to an extent which limits thepotential for reducing the signal due to background inhomogeneity.

Determining the presence or concentration of one or more analytes in asample, whether the sample is coloured or substantially clear, may beuseful since this may allow lower grade materials having a degree ofcoloration to be used for the porous strip 5 of a lateral flow device10, 25. In this way, the material cost of a lateral flow device 10, 25may be reduced, and additionally the environmental impact of producingfibres having a high degree of whiteness (for example using chemicalbleaching) may be reduced.

In general, concentrations of K−1 different analytes may be determined,whilst correcting for inhomogeneity of a porous strip 5 or similarsource of background scattering, by processing a sample image I^(S)obtained using an image sensor 2 having K different colour channels.Some of the K−1 analytes may not be of direct interest, for example,some of the K−1 analytes may be substances or compositions which providethe coloration of a sample 3, for example dyes. However, accounting foranalytes providing coloration of a sample 3 can allow more accuratedetection and quantification of one or more analytes of interestcontained in or supported on the sample 3.

A sample 3 may in general include K−1 analytes. The second method may beapplied to determine the presence or concentration of K−1 analytes whenthe image sensor 2 used to obtain sample images I^(S) has K colourchannels. The number K−1 of analytes is one less than the number K ofcolour channels to allow correction for scattering from the backgroundinhomogeneity of a porous strip 5, cuvette 70, test well 77, suspendedparticulate matter 72, or any similar source of background scattering.Some of the analytes may be substances or compositions which give riseto the coloration of a sample. Quantifying substances or compositionswhich give rise to sample coloration may not be of direct interest,however, it can allow more sensitive detection and/or more accuratequantification of one or more analytes of interest contained within acoloured sample such as urine, blood, and so forth.

A sample image I^(S) (or first image) is obtained or received in thesame way as the first method and, in the same way as the first methodcontains an image of the sample 3.

Mono-colour arrays L¹, . . . , L^(k), . . . , L^(K) corresponding toeach of the colour channels are extracted from the sample image I^(S).All of the mono-colour arrays L^(k) have the same number of entriesN_(e), and each entry is determined by aggregating one or more pixels ofthe first image in the same way as the first method. It is also possibleto apply the second method to mono-colour images I¹, . . . , I^(k), . .. , I^(K). However, in practice this may be neither necessary nordesirable since the subsequent processing of the second method is morecomplex. Each entry of the mono-colour arrays L^(k) is an aggregation ofone or more pixel intensity values I_(n,m,k).

The second method requires corresponding absorbance values to beestimated. A set of mono-colour absorbance arrays A¹, . . . , A^(k), . .. , A^(K) corresponding to each colour channel is determined. Eachmono-colour absorbance array A^(k) includes a number N_(e) of entriesA^(k) _(i) which correspond to the entries of the mono-colour arrayL^(k). Direct determination of absorbance values from sample imagesI^(S) may be difficult because the incident and transmitted/reflectedflux values may be difficult to determine in an imaging arrangement.

However, when the sample 3 is a porous strip 5 of a lateral flow testdevice 10, 25, the mono-colour absorbance arrays A¹, . . . , A^(k), . .. , A^(K) may be estimated from a sample image I^(S) encompassing a testregion 7 and surrounding regions of untreated porous strip 5.

Referring also to FIGS. 25 to 34 a method of obtaining values for themono-colour absorbance arrays A¹, . . . , A^(k), . . . , A^(K) from aporous strip 5 of a lateral flow device 10, 25 is explained withreference to theoretically modelled organic photodetector (OPD) signalsfor a system including blue dye in addition to gold nanoparticles. Inthe modelled system, the image sensor 2 is taken to be an array of OPDs,however, the image sensor 2 may use any other type of photodetector suchas a charge couple device CCD or other type of light sensor typicallyemployed in a camera.

Referring in particular to FIG. 25, a model for generating theoreticalOPD signals is based on a representative OPD absorption profile 90,which is a function of wavelength λ, in combination with representativeLED emission profiles 91, 92, 93, which are each functions of wavelengthλ. The first LED emission profile 91 corresponds to a typical green OLEDas a light source 9, the second LED emission profile 92 corresponds to atypical red OLED as a light source 9, and the third LED emission profile93 corresponds to a typical near infrared (NIR) OLED as a light source9. The OLED emission profiles 91, 92, 93 may equivalently be consideredas transmission profiles of a mosaic filter (see e.g. profiles 32, 33,34, 35 in FIG. 6) in a case where uniform white light is used as a lightsource 9 to illuminate a sample 3, without significantly affecting theinterpretation of the theoretical model.

Referring in particular to FIG. 26, further inputs to the model forgenerating theoretical OPD signals include representative absorptionprofiles 94, 95, 96 for gold nanoparticles, a blue dye andnitrocellulose fibres 36 respectively. The first absorption profile 94is a wavelength λ dependent function corresponding to the absorbance ofgold nanoparticles. The second absorption profile 95 is a wavelength λdependent function corresponding to the absorbance the blue dye. Thethird absorption profile 96 is a wavelength λ dependent functioncorresponding to the absorbance of nitrocellulose fibres 36 forming aporous strip 5.

Referring in particular to FIG. 27, further inputs to the model forgenerating theoretical OPD signals include assumed concentrationprofiles 97, 98, 99 of gold nanoparticles, blue dye and nitrocellulosefibres respectively. In the model, it is assumed that the lateral flowtest device 25 is back-illuminated and that the light transmittedthrough the porous strip 5 is imaged using an image sensor 2 composed ofa number of OPDs.

The X-axis of FIG. 27 is distance in units of pixels of the image sensor2. The first assumed concentration profile 97, plotted against theprimary Y-axis (range 0 to 1.2), corresponds to a position dependentconcentration of gold nanoparticles. The second assumed concentrationprofile 98, plotted against the primary Y-axis (range 0 to 1.2),corresponds to a position dependent concentration of blue dye. The thirdassumed concentration profile 99, plotted against the secondary Y-axis(range 0.9 to 1.02), corresponds to a position dependent concentrationof nitrocellulose fibres 36. The third assumed concentration profile 99includes fluctuations of the nitrocellulose fibre 36 concentration(meaning the density such, for example, fibre volume fraction) withposition along the porous strip 5. Also indicated in FIG. 27 is anillumination profile 100 representing a position varying illuminationintensity along the length of the porous strip 5. The illuminationprofile 100 is assumed to be the same for modelled green, red and NIROLEDS.

Referring in particular to FIG. 28, simulated OPD signals 101, 102, 103corresponding to light from green, red and NIR OLEDs respectively may beestimated based on the emission/transmission profiles 91, 92, 93,illumination profile 100, concentration profiles 97, 98, 99 andabsorbance profiles 94, 95, 96. Noise generated based on pseudo-randomnumbers was added to simulated OPD signals 101, 102, 103 to simulate OPDnoise.

Referring in particular to FIG. 29, a simulated green OPD signal 101 bis shown which is calculated for a case in which the blue dyeconcentration profile 98 was set to zero everywhere.

As a first step in extracting green absorbance values, a slowly varyingbackground profile 104, plotted against the primary Y-axis (range 0 to4500), is fitted to the simulated green OPD signal 101 b, plottedagainst the primary Y-axis (range 0 to 4500). The background profile 104represents an approximation to the average intensity, T₀, transmitted bythe nitrocellulose fibres 36 of the porous strip 5. The simulated greenOPD signal 101 b represents the transmitted intensity, T, through theporous strip 5 and the gold nanoparticles. A normalised greentransmission profile 105 is calculated as T/T₀, plotted against thesecondary Y-axis (range 0 to 1.2). It may be observed that thenormalised green transmission profile 105 retains fluctuations resultingfrom the point-to-point fluctuations in the nitrocellulose fibre 36concentration profile 99.

Referring in particular to FIG. 30, a simulated NIR OPD signal 103 b isshown which is calculated for a case in which the blue dye concentrationprofile 98 is zero everywhere.

As a first step in extracting IR absorbance values, a slowly varyingbackground profile 104, plotted against the primary Y-axis (range 0 to4500) is fitted to the simulated NIR OPD signal 103 b, plotted againstthe primary Y-axis (range 0 to 4500). Given the present modellingassumptions, the background profile 104 is the same for green and NIRdata. However, in practice the background profile 104 may vary fordifferent wavelengths λ of light, for example, when multiple lightsources illuminate the sample 3. A normalised NIR transmission profile106 is calculated as T/T₀, plotted against the secondary Y-axis (range 0to 1.2).

Referring in particular to FIGS. 31 and 32, the normalised transmissionprofiles 105, 106 are converted to absorbance values according to theformula A=−log₁₀(T/T₀). A first simulated absorbance profile 107 isobtained corresponding to the green OLED and comprising green absorbancevalues A_(G)(x) at pixel position x. A second simulated absorbanceprofile 108 comprising NIR absorbance values A_(NIR)(x) is obtainedcorresponding to the NIR OLED. The absorbance values calculated in thisfashion are more strictly viewed as changes in absorbance relative to aperfectly uniform nitrocellulose strip having the same concentration(density/fibre volume fraction) as the average concentration(density/fibre volume fraction) of the porous strip 5. Such values mayalso be referred to as delta-optical density or ΔOD values. Although thecalculation has been outlined with reference to a transmission geometry,analogous calculations may be performed for a reflection geometry.

Although the method of obtaining absorbance values has been explained inrelation to a one-dimensional model, the model may be extended toencompass two-dimensional variations in concentrations.

The entries A^(k) _(i) of each mono-colour absorbance array A^(k) may bedetermined by summing or averaging the estimated absorbance valuescorresponding to several pixel positions, for example summing A_(G)(x)or A_(NIR)(x) across several pixel positions. In general, each entryA^(k) _(i) corresponds to an entry of a mon-colour array L^(k) _(i).

Alternatively, each entry A^(k) _(i) of each mono-colour absorbancearray A^(k) may be estimated using a scatterplot of two or more sets ofestimated absorbance values to determine absorbance “fingerprint” valuesas described hereinafter. For example, absorbance fingerprints may beobtained for each of several test regions 7 of a single porous strip 5.

Referring in particular to FIGS. 33 and 34, the estimation of absorbancefingerprint values is illustrated. Estimation of absorbance fingerprintvalues is mainly of interest for obtaining coefficients of thedeconvolution matrix of Equation (15) explained hereinafter. Both ofFIGS. 33 and 34 are scatter plots of the green simulated absorbanceprofile 107 plotted against the X-axis and the NIR simulated absorbanceprofile 108 against the Y-axis. Each data point 109 represents a pair ofa green absorbance value A_(G)(x) and a NIR absorbance value A_(NIR)(x)at a particular position x of a simulated porous strip 5.

Two distinct correlations having different slopes may be observed inFIGS. 33 and 34. A first correlation is most easily seen in FIG. 34 andhas approximately unitary slope. This corresponds to the nitrocellulosefibres, the interaction of which with green and NIR wavelengths isessentially the same in the model. By examining the extremal data pointsno of the first correlation, a pair of absorbance values attributable tothe fluctuations in the nitrocellulose fibre 36 concentration profile99, also referred to as the absorbance “fingerprint” of thenitrocellulose fibres 36 within the region of porous strip 5corresponding to the scatterplot, may be estimated as A^(G) _(NC)≈0.01,A^(NIR) _(NC)≈0.01, or alternately A_(NC)≈(0.01, 0.01) using a vectornotation.

A second correlation is most easily seen in FIG. 33 and has a muchshallower slope representing the relatively strong response of the greenlight to the gold nanoparticles in comparison to the relatively weakresponse of the NIR light to the gold nanoparticles. In a similarfashion to the first correlation, for the second correlation anabsorbance “fingerprint” corresponding to the gold nanoparticles may beestimated as A^(G) _(NC)≈1, A^(NIR) _(NC)≈0.02, or A_(Au)≈(1, 0.02)using a vector notation, based on the extremal points in and subtractingthe signal due to variations in the nitrocellulose fibre 36concentration profile 99. This method of estimating absorbancefingerprints may be extended to three or more wavelength bands of light,for example, by using 3D plots or N-dimensional analysis methods.

In this way, mono-colour absorbance arrays A¹, . . . , A^(k), . . . ,A^(K) having entries A^(k) _(i) in the form of absorbance fingerprintvalues may be determined for each of N_(e) entries. Although the methodof obtaining absorbance values described with reference to the simulatedOPD signals 101, 102, 103 has been described with reference to simulatedtransmission data, the same method (with minor variations) is expectedto be equally applicable to measured data, whether obtained intransmission or reflection geometries.

Other methods of converting mono-colour arrays L¹, . . . , L^(k), . . ., L^(K) into corresponding mono-colour absorbance arrays A¹, . . . ,A^(k), . . . , A^(K) may be used, in particular when the sample 3 is nota porous strip 5. Mono-colour absorbance arrays A¹, . . . , A^(k), . . ., A^(K) having entries A^(k) _(i) in the form of absorbance valuesmeasured according to any suitable method may be analysed in accordancewith the equations set out hereinafter.

In general, each mono-colour absorbance array entry A^(k) _(i)corresponds to a range of wavelengths which are detected by the k^(th)of K colour channels. In effect, a mono-colour absorbance array entryA^(k) _(i) represents an integral across the wavelength rangetransmitted by the corresponding filter of the k^(th) colour channel(see FIG. 6). A mono-colour absorbance array entry A^(k) _(i)corresponding to the k^(th) of K colour channels may be viewed as thesum:

$\begin{matrix}{A_{i}^{k} = {s_{i}^{k} + {\sum\limits_{j = 1}^{K - 1}\;{ɛ_{j}^{k}c_{j}}}}} & (7)\end{matrix}$in which s^(k) _(i) is the absorbance in the k^(th) colour channel dueto scattering from background inhomogeneity of the porous strip 5 orother source of background scattering, c_(i,j) is the concentration ofthe j^(th) analyte out of K−1 analytes at the location corresponding tomono-colour absorbance array entry A^(k) _(i) and ß^(k) _(j) is acoefficient relating the concentration c_(i,j) to the absorbance of thej^(th) analyte out of K−1 analytes within the k^(th) colour channel. Theconcentrations c_(i,j) are expressed in units of absorbance (opticaldensity) corresponding to a reference colour channel, for example, the1^(st) colour channel k=1. Thus, the coefficients ß^(k) _(j) are each aratio of the absorbance of the j^(th) analyte between the 1^(st) andk^(th) colour channels.

An absorbance column vector A_(i) corresponding to the i^(th) of N_(e)regions of the sample image I^(S) may be constructed using thecorresponding mono-colour absorbance array entries A^(k) _(i) for allcolour channels:

$\begin{matrix}{A_{i} = \begin{pmatrix}A_{i}^{1} \\A_{i}^{2} \\M \\A_{i}^{K}\end{pmatrix}} & (8)\end{matrix}$and similarly, a concentration column vector c_(i) may be defined as:

$\begin{matrix}{c_{i} = \begin{pmatrix}c_{i,1} \\c_{i,2} \\M \\c_{i,{K - 1}} \\c_{i,s}\end{pmatrix}} & (9)\end{matrix}$in which the concentration c_(i,s) corresponding to the backgroundabsorbance s^(k) _(i) is a dummy concentration which is set to thebackground absorbance in the reference colour channel, for example s¹_(i) corresponding to the 1^(st) colour channel k=1. The use of thedummy concentration in equivalent units to the analyte concentrationsc_(i,j) maintains appropriate scaling of measured absorbance valuesthroughout the calculations described hereinafter. In practice, asexplained hereinafter, calibration of the method typically includesobtaining measurements of the background scattering without anyanalytes, so obtaining a suitable value for the dummy concentrationc_(i,s) is not problematic. The absorbance vector A_(i) may be expressedin terms of the coefficients ε^(k) _(j) background absorbance s^(k) _(i)and concentration vector c_(i) using a matrix equation:

$\begin{matrix}{{\begin{pmatrix}A_{i}^{1} \\A_{i}^{2} \\M \\A_{i}^{K - 1} \\A_{i}^{K}\end{pmatrix} = {\begin{pmatrix}ɛ_{1}^{1} & ɛ_{2}^{1} & \Lambda & ɛ_{K - 1}^{1} & s_{i}^{1} \\ɛ_{1}^{2} & ɛ_{2}^{2} & \Lambda & ɛ_{K - 1}^{2} & s_{i}^{2} \\M & M & O & M & M \\ɛ_{1}^{K - 1} & ɛ_{2}^{K - 1} & \Lambda & ɛ_{K - 1}^{K - 1} & s_{i}^{K - 1} \\ɛ_{1}^{K} & ɛ_{2}^{K} & \Lambda & ɛ_{K - 1}^{K} & s_{i}^{K}\end{pmatrix}\begin{pmatrix}c_{i,1} \\c_{i,2} \\M \\c_{i,{K - 1}} \\c_{i,s}\end{pmatrix}}}{A = {Mc}}} & (10)\end{matrix}$in which M is a square matrix having coefficients M_(k,j)=ε^(k) _(j) for1≤j≤K−1 and M_(k,j)=s^(k) _(j) for j=K. By inverting the matrix M,unknown concentrations c_(i) of analytes corresponding to the i^(th) ofN_(e) regions of the sample image I^(S) may be determined from themono-colour absorbance arrays A¹, . . . , A^(k), . . . , A^(K) accordingto:c _(i) =M ⁻¹ A _(i)  (11)

In order to apply Equation (11), it is necessary to know thecoefficients M_(k,j) of the matrix M, so that the inverse M⁻¹ may becalculated. When evaluating Equation (11), a value calculatedcorresponding to the background scattering “concentration” would ideallybe equal to the corresponding dummy concentration c_(i,s). The dummyconcentration may be zero when absorbance values are estimated withreference to the average absorbance of a porous strip 5, as describedhereinbefore. In practical circumstances, the value calculatedcorresponding to the background scattering “concentration” may deviatefrom the dummy concentration c_(i,s). The size of the deviation mayprovide an indication of variations between different porous strips 5,cuvettes 71, test wells 77, and so forth. A large deviation may providean indication of possible problems with a particular sample 3 or withthe calibration of the matrix M coefficients M_(k,j).

The coefficients M_(k,j) of the matrix M may be determined fromexperimental measurements using calibration samples 54 with knownconcentration distributions c_(i,j) of each analyte. Preferably,calibration regions 56 of a calibration sample 54 have substantiallyuniform concentration throughout. A measured set of absorbance valuesfrom a first calibration sample 54 may be represented by the referenceabsorbance vector A*₁ and the corresponding reference concentrations bythe reference concentration vector c*₁. In general, for a number K ofcolour channels, a number K of calibration samples 54 and measurementsare required. Alternatively, a single calibration sample 54 may includea number K of different calibration regions 56, each corresponding to adifferent calibration vector c*. A fingerprint matrix F may definedusing the set of reference absorbance vectors A*₁, . . . , A*_(k) bysetting the coefficients of each reference absorbance vector A*₁, . . ., A*_(k) as the coefficients for a corresponding column of thefingerprint matrix F:

$\begin{matrix}{F = \begin{pmatrix} \uparrow & \uparrow & \; & \uparrow \\A_{1}^{*} & A_{2}^{*} & \Lambda & A_{K}^{*} \\ \downarrow & \downarrow & \; & \downarrow \end{pmatrix}} & (12)\end{matrix}$and the corresponding calibration concentration vectors c₁, . . . ,c_(K) may be set as the columns of a calibration matrix C:

$\begin{matrix}{C = \begin{pmatrix} \uparrow & \uparrow & \; & \uparrow \\c_{1} & c_{2} & \Lambda & c_{N} \\ \downarrow & \downarrow & \; & \downarrow \end{pmatrix}} & (13)\end{matrix}$and the fingerprint matrix F and calibration matrix C are relatedaccording to:F=MC  (14)

The coefficients M_(k,j) of the matrix M can then be calculated asM=FC⁻¹, and the coefficients of the inverse matrix M⁻¹ can be calculatedas M⁻¹=CF⁻¹. Thus, a set of unknown concentrations represented by aconcentration vector c_(i) may be recovered using CF⁻¹ as adeconvolution matrix for the estimated absorbance values represented byan absorbance vector A_(i) according to:c _(i) =CF ⁻¹ A _(i)  (15)

In this way, a set of unknown concentrations c_(i,j) of K−1 analytes maybe reconstructed from the estimates of the mono-colour absorbance arrayentries A^(k) _(i) estimated from the sample image I^(S) and acalibration image I^(C). Where the sample 3 is a porous strip 5, themono-colour absorbance array entries A^(k) _(i) may be estimated bynormalisation to a slowly varying background 104 as described inrelation to FIGS. 29 and 30.

The actual physical concentration or number density of each analyte, forexample in units of number·cm⁻³, can be estimated from the reconstructedconcentrations (i.e. absorbance values at the reference wavelength)using the Beer-Lambert law if the path length through the sample 3 andan attenuation coefficient for the j^(th) analyte is known for thereference colour channel. If the attenuation coefficient for the j^(th)analyte is not known for the reference colour channel, then thecoefficients M_(k,j)=ε^(k) _(j) (calculated by inverting thedeconvolution matrix to obtain M=FC⁻¹) may be used to convert theconcentration (absorbance) c_(i,j) in terms of absorbance in thereference colour channel to an absorbance for a colour channel for whichan attenuation coefficient is known.

In some examples, it may be convenient to normalise absorbance valueswith respect to a single reference calibration value, for example, A*₁.For example, with normalisation relative to A*₁, a normalisedfingerprint matrix F_(n) may be expressed as:

$\begin{matrix}{F = \begin{pmatrix}1 & \frac{A_{2}^{*^{1}}}{A_{1}^{*^{1}}} & \Lambda & \frac{A_{K}^{*^{1}}}{A_{1}^{*^{1}}} \\\frac{A_{1}^{*^{2}}}{A_{1}^{*^{1}}} & \frac{A_{2}^{*^{2}}}{A_{1}^{*^{1}}} & \Lambda & \frac{A_{K}^{*^{2}}}{A_{1}^{*^{1}}} \\M & M & O & M \\\frac{A_{1}^{*^{K}}}{A_{1}^{*^{1}}} & \frac{A_{2}^{*^{K}}}{A_{1}^{*^{1}}} & \Lambda & \frac{A_{K}^{*^{K}}}{A_{1}^{*^{1}}}\end{pmatrix}} & \left( {12b} \right)\end{matrix}$

Each of Equations 7 to 15 may be normalised in this manner, to allowabsorbance and concentration values to be expressed as fractions withrespect to a reference calibration value, for example A*₁.

Determination of Concentration and Calibration Matrix Values

The calibration is simplified in the case that pure (or substantiallypure) samples of the K−1 different analytes having known concentrationsare available for testing in reference conditions, for example,supported on a porous strip 5, or contained within a cuvette 71, testwell 77, and so forth. In the following discussion, location/regionindex i is dropped for brevity. One of the calibration samples 54 orregions 56 should ideally correspond to only the background scattering,i.e. the porous strip 5, cuvette 71, test well 77, and so forth. In thiscase, determining the calibration matrix is simplified, since thedetermination of the concentration c_(j) for each analyte for thereference colour channel can be simplified. For example, if the K^(th)calibration sample 54 or region 56 includes only the backgroundscattering, then a calibration concentration c_(j) ^(o) of the j^(th)calibration sample (1≤j≤K−1), which includes the pure (or substantiallypure) j^(th) analyte, using the 1st colour channel as the referencecolour channel, may be approximated as:c _(j) ⁰ =A _(j) ¹ −A _(K) ¹  (16)

In which A¹ _(j) is the measured absorbance of the pure or substantiallypure sample of the j^(th) analyte corresponding to the 1^(st) colourchannel. The calibration matrix C may be written as:

$\begin{matrix}{C = \begin{pmatrix}c_{1}^{0} & 0 & \Lambda & 0 & 0 \\0 & c_{2}^{0} & \Lambda & 0 & 0 \\M & M & O & M & M \\0 & 0 & 0 & c_{K - 1}^{0} & 0 \\c_{s} & c_{s} & c_{s} & c_{s} & c_{s}\end{pmatrix}} & (17)\end{matrix}$

In which the dummy concentration c_(s)=A¹ _(K). In this special case,the calculation of the deconvolution matrix CF⁻¹ may be simplified.

The calibration matrix C and the calculation of the deconvolution matrixCF⁻¹ may be simplified further if the absorbance of pure (orsubstantially pure) samples of the different analytes may be testedunder conditions in which the background scattering is very low ornegligible.

Application to One Analyte and Background Scattering

Simulations were conducted using the model described hereinbefore withreference to FIGS. 25 to 32 in a case where the blue dye concentrationprofile 98 was equal to zero at every position. The resulting simulatedOPD signals 101 b, 103 b are as shown in FIGS. 29 and 30. Theconcentration values were chosen corresponding to absorbance fingerprintvalues, and taking the values corresponding to the simulated green OLED(or green filter) as reference values. A first simulated calibrationsample corresponding to gold nanoparticles having an optical density ofOD=1 may be represented in the method by the concentration vector c_(Au)^(T)=(1, 0) and the corresponding absorbance vector is A_(Au) ^(T)=(1,0.02). The relevant absorbance values were obtained as absorbancefingerprint values as described hereinbefore with reference to FIGS. 33and 34. A second simulated calibration sample, corresponding to a blankporous strip 5 in the form of a nitrocellulose strip, may be representedin the method by the absorbance vector A_(NC) ^(T)=(0.01, 0.01), so thatthe dummy concentration is c_(s)=0.01 and the correspondingconcentration vector is c_(NC) ^(T)=(0, 0.01). The relevant absorbancevalues were obtained as absorbance fingerprint values, as describedhereinbefore with reference to FIGS. 33 and 34. Thus, taking the greenOLED wavelength range (see FIG. 25) as the reference, the calibrationmatrix C and fingerprint matrix F according to Equations 12 and 13 maybe written as:

$\begin{matrix}{C = {{\begin{pmatrix}1 & 0 \\0 & 0.01\end{pmatrix}\mspace{14mu} F} = \begin{pmatrix}1 & 0.01 \\0.02 & 0.01\end{pmatrix}}} & (18)\end{matrix}$

The deconvolution matrix CF⁻¹ of Equation 15 may be calculated byinverting the fingerprint matrix F:

$\begin{matrix}{{{CF}^{- 1} = {\begin{pmatrix}1 & 0 \\0 & 0.01\end{pmatrix}\begin{pmatrix}1.020 & {- 1.020} \\{- 2.041} & 102.041\end{pmatrix}}}{{CF}^{- 1} = \begin{pmatrix}1.020 & {- 1.020} \\{- 0.020} & 1.020\end{pmatrix}}} & (19)\end{matrix}$and substituting the deconvolution matrix CF⁻¹ into Equation 15 yields:

$\begin{matrix}{\begin{pmatrix}c_{Au} \\c_{NC}\end{pmatrix} = {\begin{pmatrix}1.020 & {- 1.020} \\{- 0.0020} & 1.020\end{pmatrix}\begin{pmatrix}A_{green} \\A_{NIR}\end{pmatrix}}} & (20)\end{matrix}$

Thus, the concentration c^(Au) of gold nanoparticles, in this exampleexpressed in terms of absorbance in OD, is given asc_(Au)=1.02(A_(green)−A_(NIR)), which is essentially the same resultapplied in Equation (4) of the first method.

Application to One Analyte and Background Scattering with a Coloured Dye

Simulations were also conducted using the model described hereinbeforewith reference to FIGS. 25 to 32 in a case where the blue dyeconcentration profile 98 was as shown in FIG. 27. The resultingsimulated OPD signals 101, 102, 103 are shown in FIG. 28. Theconcentration values were chosen as absorbance values using the greenLED emission wavelengths as reference.

Referring also to FIG. 35, application of the simple two-colourdifference method (see Equation (4)) to absorbance values obtained basedon the simulated OPD signals 101, 102, 103 leads to inaccuracy indetermining the change in absorbance due to the gold nanoparticles whenonly the green and NIR simulated OPD signals 101, 103 are considered.

The total, summed absorbance 112 is represented by a solid line. Theestimated gold nanoparticle concentration 113 is represented by a dottedline. The estimated background scattering from the nitrocellulose strip114 is represented by the dashed line.

In particular, the presence of the blue dye leads to errors in theestimated gold nanoparticle concentration 113. In particular, thebaseline absorbance around the location of the gold nanoparticles isdistorted by absorbance of the blue dye. The problem is that there arethree unknowns in the concentration values, namely, the goldnanoparticle concentration c_(Au), the blue dye concentration c_(dye)and the background scattering c_(NC) from the nitrocellulose strip.Using green and NIR OLEDs, there are only two measurements. The solutionis to increase the number of wavelength ranges to three.

The second method utilising the deconvolution method may be applied ifall three of the simulated OPD signals 101, 102, 103 are utilised. Afirst simulated calibration sample, corresponding to gold nanoparticleshaving an optical density of OD=1, may be represented in the method bythe concentration vector c_(Au) ^(T)=(1, 0, 0) (c_(Au), c_(dye), c_(NC))and the corresponding absorbance vector is A_(AU) ^(T)=(1, 0.17, 0.02)(green, red, NIR). The relevant absorbance values were obtained asabsorbance fingerprint values according to a method analogous to thatdescribed hereinbefore with reference to FIGS. 33 and 34. A secondsimulated calibration sample, corresponding to the blue dye, may berepresented in the method by the concentration vector c_(dye) ^(T)=(0,0.024, 0) and the corresponding absorbance vector is A_(Au) ^(T)=(0.024,0.89, 0). The relevant absorbance values were obtained as absorbancefingerprint values according to a method analogous to that describedhereinbefore with reference to FIGS. 33 and 34. A third simulatedcalibration sample, corresponding to a blank porous strip, has anabsorbance vector of A_(NC) ^(T)=(0.01, 0.01, 0.01), so that the dummyconcentration c_(s)=0.01 and the corresponding concentration vector isc_(NC) ^(T)=(0, 0, 0.01). The relevant absorbance values were obtainedas absorbance fingerprint values according to a method analogous to thatdescribed hereinbefore with reference to FIGS. 33 and 34. Thus, takingthe green wavelength as reference wavelength, the calibration matrix Cand fingerprint matrix F according to Equations 12 and 13 may be writtenas:

$\begin{matrix}{c = {{\begin{pmatrix}1 & 0 & 0 \\0 & 0.024 & 0 \\0 & 0. & 0.01\end{pmatrix}\mspace{14mu} F} = \begin{pmatrix}1 & 0.024 & 0.01 \\0.17 & 0.89 & 0.01 \\0.02 & 0 & 0.01\end{pmatrix}}} & (21)\end{matrix}$

The deconvolution matrix CF⁻¹ of Equation 15 may be calculated byinverting the fingerprint matrix F:

$\begin{matrix}{{{CF}^{- 1} = {\begin{pmatrix}1 & 0 & 0 \\0 & 0.024 & 0 \\0 & 0. & 0.01\end{pmatrix}\begin{pmatrix}1.025 & {- 0.028} & {- 0.997} \\{- 0.173} & 1.128 & {- 0.956} \\{- 2.049} & 0.055 & 101.994\end{pmatrix}}}{{CF}^{- 1} = \begin{pmatrix}1.025 & {- 0.028} & {- 0.997} \\{- 0.004} & 0.027 & {- 0.023} \\{- 0.02} & 0.001 & 1.020\end{pmatrix}}} & (22)\end{matrix}$and substituting the deconvolution matrix CF⁻¹ into Equation 15 yields:

$\begin{matrix}{\begin{pmatrix}c_{Au} \\c_{dye} \\c_{NC}\end{pmatrix} = {\begin{pmatrix}1.025 & {- 0.028} & {- 0.997} \\{- 0.004} & 0.027 & {- 0.023} \\{- 0.02} & 0.001 & 1.020\end{pmatrix}\begin{pmatrix}A_{green} \\A_{red} \\A_{NIR}\end{pmatrix}}} & (23)\end{matrix}$

Thus, the concentration c_(Au) of gold nanoparticles, in this exampleexpressed in terms of change in absorbance in OD, is given asc_(Au)=1.025A_(green)−0.028A_(red)−0.997A_(NIR)). This result may beapplied to estimated absorbance values corresponding to a sample 3without the need to plot a scatterplot to determine an absorbancefingerprint.

Referring also to FIG. 36, the total, summed absorbance 112 isrepresented by a solid line. The estimated gold nanoparticleconcentration 113 is represented by a dotted line. The estimatedbackground scattering from the nitrocellulose strip 115 is representedby the dashed line. The estimated concentration of the blue dye 115 isrepresented by the chained line.

It can be seen that applying the second method using three colourchannels (green, red and NIR) is expected to allow for clear separationof the change in absorbance due to the gold nanoparticles, blue dye andthe nitrocellulose strip. In particular, the estimated gold nanoparticleconcentration 113 and the estimated concentration of the blue dye 115are expected to be separable.

MODIFICATIONS

It will be appreciated that many modifications may be made to theembodiments hereinbefore described. Such modifications may involveequivalent and other features which are already known in relation tocolorimetric analysis and which may be used instead of or in addition tofeatures already described herein. Features of one embodiment may bereplaced or supplemented by features of another embodiment.

For example, the preceding methods have been described in relation tostill images. However, the methods may equally be applied to some oreach frame of a video. In other words, the sample images I^(S) may beextracted as the whole image or sub-regions 52, 57 of an individualframe of a video. In this way, colorimetric analysis may be dynamic. Forexample, the rate of development of a colour associated with an analytemay be determined for the test region 7 of a lateral flow device 10, 25.

Although claims have been formulated in this application to particularcombinations of features, it should be understood that the scope of thedisclosure of the present invention also includes any novel features orany novel combination of features disclosed herein either explicitly orimplicitly or any generalization thereof, whether or not it relates tothe same invention as presently claimed in any claim and whether or notit mitigates any or all of the same technical problems as does thepresent invention.

The applicant hereby gives notice that new claims may be formulated tosuch features and/or combinations of such features during theprosecution of the present application or of any further applicationderived therefrom.

The invention claimed is:
 1. A method comprising: determining thepresence or concentration of one or more analytes in a sample,comprising: receiving a first image containing an image of the sample,the first image obtained using an image sensor comprising detectorsarranged in rows and columns, the image sensor having two or more colourchannels; extracting, from the first image, a mono-colour arraycorresponding to each colour channel, wherein each mono-colour arraycomprises one or more entries and each entry is determined byaggregating one or more pixels of the first image; determining amono-colour absorbance array corresponding to each colour channel,wherein each entry of a mono-colour absorbance array corresponding to agiven colour channel is determined by calculating an absorbance valuebased on the corresponding entry of the mono-colour array of the givencolour channel; determining, for each entry of the mono-colourabsorbance arrays, a concentration vector by: generating an absorbancevector using the absorbance values from corresponding entries of each ofthe mono-colour absorbance arrays; determining the concentration vectorby multiplying the absorbance vector with a de-convolution matrix;wherein each concentration vector includes a concentration valuecorresponding to each of the one or more analytes.
 2. A method accordingto claim 1, wherein each entry of each mono-colour array corresponds to:an aggregate of a row or a column of the first image; an aggregate ofthe pixels of the first image within a region of interest; or a singlepixel of the first image, wherein each mono-colour array is amono-colour image.
 3. A method according to claim 1, wherein receivingthe first image comprises using the image sensor to obtain the firstimage.
 4. A method according to claim 1, wherein the image sensorcomprises red, green and blue colour channels.
 5. A method according toclaim 1, wherein the image sensor comprises an infra-red colour channel.6. A method comprising applying the method according to claim 1 to eachframe of a video, wherein receiving a first image comprises extracting aframe from the video.
 7. A method according to claim 3, wherein thesample is illuminated by ambient light.
 8. A method according to claim3, further comprising illuminating the sample using a light source,wherein the sample and image sensor are arranged to be screened fromambient light.
 9. A method according to claim 3, further comprisingarranging the sample within a sample holder having a fixed geometricrelationship with the image sensor.
 10. A method according to claim 1,wherein the first image is obtained using light transmitted through thesample.
 11. A method according to claim 1, wherein the first image isobtained using light reflected from the sample.
 12. A method accordingto claim 1, wherein the image sensor forms part of a mobile device. 13.A method according to claim 12, wherein the mobile device comprises oneor more processors, and wherein the step of determining the presence orconcentration of one or more analytes is carried out by the one or moreprocessors.
 14. A method according to claim 1, wherein receiving thefirst image comprises: receiving a full sensor image which contains theimage of the sample; identifying a first sub-region of the full sensorimage which contains the sample; obtaining the first image by extractingthe first sub-region.
 15. A method of determining a de-convolutionmatrix, the method comprising: providing a number, K, of calibrationsamples, wherein each calibration sample comprises a known concentrationof K different analytes; for each calibration sample: determining, foreach of a number K of colour channels, the absorbance values of thecalibration sample; generating an absorbance vector using the number Kof absorbance values; generating a concentration vector using the numberK of known concentrations of analytes; generating a first K by K matrixby setting the values of each column, or each row, to be equal to thevalues of the absorbance vector corresponding to a given calibrationsample; inverting the first matrix; generating a second K by K matrix bysetting the values of each column, or each row, to be equal to thevalues of the concentration vector corresponding to a given calibrationsample; determining a deconvolution matrix by multiplying the secondmatrix by inverse of the first matrix.
 16. A method according to claim3, wherein the sample is illuminated by a broadband light source.
 17. Amethod according to claim 3, wherein the sample is illuminated by awhite light source.